TSTP Solution File: ITP050^1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : ITP050^1 : TPTP v8.2.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon May 20 22:48:49 EDT 2024
% Result : Theorem 24.92s 3.99s
% Output : Refutation 25.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 1182
% Syntax : Number of formulae : 4066 ( 564 unt; 236 typ; 0 def)
% Number of atoms : 67482 (8144 equ; 0 cnn)
% Maximal formula atoms : 12 ( 17 avg)
% Number of connectives : 14328 (5491 ~;6292 |; 620 &; 0 @)
% ( 655 <=>;1270 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Number of types : 10 ( 9 usr)
% Number of type conns : 1842 (1841 >; 1 *; 0 +; 0 <<)
% Number of symbols : 880 ( 877 usr; 662 con; 0-6 aty)
% Number of variables : 8700 ( 88 ^8057 !; 540 ?;8700 :)
% ( 15 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
product_prod_nat_nat: $tType ).
thf(type_def_6,type,
a: $tType ).
thf(type_def_7,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_8,type,
nat: $tType ).
thf(type_def_9,type,
set_Pr1986765409at_nat: $tType ).
thf(type_def_10,type,
set_nat: $tType ).
thf(type_def_11,type,
set_set_nat: $tType ).
thf(type_def_12,type,
set_se1612935105at_nat: $tType ).
thf(type_def_13,type,
list_P559422087at_nat: $tType ).
thf(type_def_14,type,
list_nat: $tType ).
thf(func_def_0,type,
set_se1612935105at_nat: $tType ).
thf(func_def_1,type,
list_P559422087at_nat: $tType ).
thf(func_def_2,type,
set_Pr1986765409at_nat: $tType ).
thf(func_def_3,type,
product_prod_nat_nat: $tType ).
thf(func_def_4,type,
set_set_nat: $tType ).
thf(func_def_5,type,
list_nat: $tType ).
thf(func_def_6,type,
set_nat: $tType ).
thf(func_def_7,type,
nat: $tType ).
thf(func_def_8,type,
a: $tType ).
thf(func_def_9,type,
edmond1517640972ysis_a: ( product_prod_nat_nat > a ) > $o ).
thf(func_def_10,type,
edmond475474835dges_a: ( product_prod_nat_nat > a ) > nat > nat > set_Pr1986765409at_nat ).
thf(func_def_11,type,
edmond771116670s_uE_a: ( product_prod_nat_nat > a ) > set_Pr1986765409at_nat ).
thf(func_def_12,type,
finite_card_nat: set_nat > nat ).
thf(func_def_13,type,
finite447719721at_nat: set_Pr1986765409at_nat > nat ).
thf(func_def_14,type,
finite_finite_nat: set_nat > $o ).
thf(func_def_15,type,
finite772653738at_nat: set_Pr1986765409at_nat > $o ).
thf(func_def_16,type,
finite2012248349et_nat: set_set_nat > $o ).
thf(func_def_17,type,
finite1457549322at_nat: set_se1612935105at_nat > $o ).
thf(func_def_18,type,
finite_Graph_a: ( product_prod_nat_nat > a ) > $o ).
thf(func_def_19,type,
e_a: ( product_prod_nat_nat > a ) > set_Pr1986765409at_nat ).
thf(func_def_20,type,
v_a: ( product_prod_nat_nat > a ) > set_nat ).
thf(func_def_21,type,
adjacent_nodes_a: ( product_prod_nat_nat > a ) > nat > set_nat ).
thf(func_def_22,type,
incoming_a: ( product_prod_nat_nat > a ) > nat > set_Pr1986765409at_nat ).
thf(func_def_23,type,
incoming_a2: ( product_prod_nat_nat > a ) > set_nat > set_Pr1986765409at_nat ).
thf(func_def_24,type,
isPath_a: ( product_prod_nat_nat > a ) > nat > list_P559422087at_nat > nat > $o ).
thf(func_def_25,type,
isShortestPath_a: ( product_prod_nat_nat > a ) > nat > list_P559422087at_nat > nat > $o ).
thf(func_def_26,type,
outgoing_a: ( product_prod_nat_nat > a ) > nat > set_Pr1986765409at_nat ).
thf(func_def_27,type,
outgoing_a2: ( product_prod_nat_nat > a ) > set_nat > set_Pr1986765409at_nat ).
thf(func_def_28,type,
pathVertices: nat > list_P559422087at_nat > list_nat ).
thf(func_def_29,type,
reachableNodes_a: ( product_prod_nat_nat > a ) > nat > set_nat ).
thf(func_def_30,type,
inf_inf_nat: nat > nat > nat ).
thf(func_def_31,type,
inf_inf_set_nat: set_nat > set_nat > set_nat ).
thf(func_def_32,type,
inf_in586391887at_nat: set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat ).
thf(func_def_33,type,
cons_nat: nat > list_nat > list_nat ).
thf(func_def_34,type,
cons_P66992567at_nat: product_prod_nat_nat > list_P559422087at_nat > list_P559422087at_nat ).
thf(func_def_35,type,
nil_Pr1308055047at_nat: list_P559422087at_nat ).
thf(func_def_36,type,
set_nat2: list_nat > set_nat ).
thf(func_def_37,type,
set_Pr2131844118at_nat: list_P559422087at_nat > set_Pr1986765409at_nat ).
thf(func_def_38,type,
size_s1990949619at_nat: list_P559422087at_nat > nat ).
thf(func_def_39,type,
ord_less_eq_nat: nat > nat > $o ).
thf(func_def_40,type,
ord_less_eq_set_nat: set_nat > set_nat > $o ).
thf(func_def_41,type,
ord_le841296385at_nat: set_Pr1986765409at_nat > set_Pr1986765409at_nat > $o ).
thf(func_def_42,type,
product_Pair_nat_nat: nat > nat > product_prod_nat_nat ).
thf(func_def_43,type,
collect_nat: ( nat > $o ) > set_nat ).
thf(func_def_44,type,
collec7649004at_nat: ( product_prod_nat_nat > $o ) > set_Pr1986765409at_nat ).
thf(func_def_45,type,
member_nat: nat > set_nat > $o ).
thf(func_def_46,type,
member701585322at_nat: product_prod_nat_nat > set_Pr1986765409at_nat > $o ).
thf(func_def_47,type,
member_set_nat: set_nat > set_set_nat > $o ).
thf(func_def_48,type,
member298845450at_nat: set_Pr1986765409at_nat > set_se1612935105at_nat > $o ).
thf(func_def_49,type,
c: product_prod_nat_nat > a ).
thf(func_def_50,type,
edges: set_Pr1986765409at_nat ).
thf(func_def_51,type,
p: list_P559422087at_nat ).
thf(func_def_52,type,
s: nat ).
thf(func_def_53,type,
t: nat ).
thf(func_def_57,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_58,type,
vAND: $o > $o > $o ).
thf(func_def_59,type,
bCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_60,type,
cCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > X1 > X0 > X2 ) ).
thf(func_def_61,type,
sCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_62,type,
vIMP: $o > $o > $o ).
thf(func_def_63,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_64,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_65,type,
iCOMB:
!>[X0: $tType] : ( X0 > X0 ) ).
thf(func_def_66,type,
vNOT: $o > $o ).
thf(func_def_67,type,
sP0: set_nat > nat > $o ).
thf(func_def_68,type,
sP1: set_Pr1986765409at_nat > nat > $o ).
thf(func_def_69,type,
sP2: nat > nat > nat > $o ).
thf(func_def_70,type,
sP3: nat > nat > nat > $o ).
thf(func_def_71,type,
sP4: nat > nat > nat > $o ).
thf(func_def_72,type,
sP5: nat > nat > nat > $o ).
thf(func_def_73,type,
sP6: list_P559422087at_nat > nat > nat > $o ).
thf(func_def_74,type,
sP7: list_P559422087at_nat > nat > nat > $o ).
thf(func_def_75,type,
sK8: set_nat > list_nat ).
thf(func_def_76,type,
sK9: set_Pr1986765409at_nat > list_P559422087at_nat ).
thf(func_def_77,type,
sK10: nat > set_nat > set_nat ).
thf(func_def_78,type,
sK11: nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat ).
thf(func_def_79,type,
sK12: ( product_prod_nat_nat > $o ) > ( product_prod_nat_nat > $o ) > product_prod_nat_nat ).
thf(func_def_80,type,
sK13: ( nat > $o ) > ( nat > $o ) > nat ).
thf(func_def_81,type,
sK14: set_nat > nat > set_nat ).
thf(func_def_82,type,
sK15: set_nat > set_nat > nat ).
thf(func_def_83,type,
sK16: set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_84,type,
sK17: set_Pr1986765409at_nat > nat > set_Pr1986765409at_nat ).
thf(func_def_85,type,
sK18: set_nat > set_set_nat > set_nat ).
thf(func_def_86,type,
sK19: set_nat > set_set_nat > set_nat ).
thf(func_def_87,type,
sK20: set_Pr1986765409at_nat > set_se1612935105at_nat > set_Pr1986765409at_nat ).
thf(func_def_88,type,
sK21: set_Pr1986765409at_nat > set_se1612935105at_nat > set_Pr1986765409at_nat ).
thf(func_def_89,type,
sK22: nat > set_nat > nat ).
thf(func_def_90,type,
sK23: nat > set_nat > nat ).
thf(func_def_91,type,
sK24: list_nat > nat > nat ).
thf(func_def_92,type,
sK25: list_nat > nat > list_nat ).
thf(func_def_93,type,
sK26: list_nat > nat > list_nat ).
thf(func_def_94,type,
sK27: set_nat > nat > set_nat ).
thf(func_def_95,type,
sK28: set_Pr1986765409at_nat > nat > set_Pr1986765409at_nat ).
thf(func_def_96,type,
sK29: list_P559422087at_nat > product_prod_nat_nat > product_prod_nat_nat ).
thf(func_def_97,type,
sK30: list_P559422087at_nat > product_prod_nat_nat > list_P559422087at_nat ).
thf(func_def_98,type,
sK31: list_P559422087at_nat > product_prod_nat_nat > list_P559422087at_nat ).
thf(func_def_99,type,
sK32: nat > list_P559422087at_nat > nat > nat ).
thf(func_def_100,type,
sK33: nat > list_P559422087at_nat > nat > nat ).
thf(func_def_101,type,
sK34: nat > list_P559422087at_nat > nat > list_P559422087at_nat ).
thf(func_def_102,type,
sK35: ( nat > nat > $o ) > nat ).
thf(func_def_103,type,
sK36: ( nat > nat > $o ) > nat ).
thf(func_def_104,type,
sK37: ( nat > nat > $o ) > nat ).
thf(func_def_105,type,
sK38: ( nat > nat > $o ) > nat ).
thf(func_def_106,type,
sK39: ( set_nat > set_nat > set_nat ) > set_nat ).
thf(func_def_107,type,
sK40: ( set_nat > set_nat > set_nat ) > set_nat ).
thf(func_def_108,type,
sK41: ( set_nat > set_nat > set_nat ) > set_nat ).
thf(func_def_109,type,
sK42: ( set_nat > set_nat > set_nat ) > set_nat ).
thf(func_def_110,type,
sK43: ( set_nat > set_nat > set_nat ) > set_nat ).
thf(func_def_111,type,
sK44: ( set_nat > set_nat > set_nat ) > set_nat ).
thf(func_def_112,type,
sK45: ( set_nat > set_nat > set_nat ) > set_nat ).
thf(func_def_113,type,
sK46: ( nat > nat > nat ) > nat ).
thf(func_def_114,type,
sK47: ( nat > nat > nat ) > nat ).
thf(func_def_115,type,
sK48: ( nat > nat > nat ) > nat ).
thf(func_def_116,type,
sK49: ( nat > nat > nat ) > nat ).
thf(func_def_117,type,
sK50: ( nat > nat > nat ) > nat ).
thf(func_def_118,type,
sK51: ( nat > nat > nat ) > nat ).
thf(func_def_119,type,
sK52: ( nat > nat > nat ) > nat ).
thf(func_def_120,type,
sK53: ( set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat ) > set_Pr1986765409at_nat ).
thf(func_def_121,type,
sK54: ( set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat ) > set_Pr1986765409at_nat ).
thf(func_def_122,type,
sK55: ( set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat ) > set_Pr1986765409at_nat ).
thf(func_def_123,type,
sK56: ( set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat ) > set_Pr1986765409at_nat ).
thf(func_def_124,type,
sK57: ( set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat ) > set_Pr1986765409at_nat ).
thf(func_def_125,type,
sK58: ( set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat ) > set_Pr1986765409at_nat ).
thf(func_def_126,type,
sK59: ( set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat ) > set_Pr1986765409at_nat ).
thf(func_def_127,type,
sK60: ( nat > $o ) > nat ).
thf(func_def_128,type,
sK61: nat > ( nat > $o ) > nat ).
thf(func_def_129,type,
sK62: list_P559422087at_nat > nat > nat > list_P559422087at_nat ).
thf(func_def_130,type,
sK63: list_P559422087at_nat > nat > nat > nat ).
thf(func_def_131,type,
sK64: list_P559422087at_nat > nat > nat > nat ).
thf(func_def_132,type,
sK65: list_P559422087at_nat > nat > nat > nat ).
thf(func_def_133,type,
sK66: list_P559422087at_nat > nat > nat > list_P559422087at_nat ).
thf(func_def_134,type,
sK67: ( set_nat > set_nat ) > set_nat ).
thf(func_def_135,type,
sK68: ( set_nat > set_nat ) > set_nat ).
thf(func_def_136,type,
sK69: ( set_nat > nat ) > set_nat ).
thf(func_def_137,type,
sK70: ( set_nat > nat ) > set_nat ).
thf(func_def_138,type,
sK71: ( set_nat > set_Pr1986765409at_nat ) > set_nat ).
thf(func_def_139,type,
sK72: ( set_nat > set_Pr1986765409at_nat ) > set_nat ).
thf(func_def_140,type,
sK73: ( nat > set_nat ) > nat ).
thf(func_def_141,type,
sK74: ( nat > set_nat ) > nat ).
thf(func_def_142,type,
sK75: ( nat > nat ) > nat ).
thf(func_def_143,type,
sK76: ( nat > nat ) > nat ).
thf(func_def_144,type,
sK77: ( nat > set_Pr1986765409at_nat ) > nat ).
thf(func_def_145,type,
sK78: ( nat > set_Pr1986765409at_nat ) > nat ).
thf(func_def_146,type,
sK79: ( set_Pr1986765409at_nat > set_nat ) > set_Pr1986765409at_nat ).
thf(func_def_147,type,
sK80: ( set_Pr1986765409at_nat > set_nat ) > set_Pr1986765409at_nat ).
thf(func_def_148,type,
sK81: ( set_Pr1986765409at_nat > nat ) > set_Pr1986765409at_nat ).
thf(func_def_149,type,
sK82: ( set_Pr1986765409at_nat > nat ) > set_Pr1986765409at_nat ).
thf(func_def_150,type,
sK83: ( set_Pr1986765409at_nat > set_Pr1986765409at_nat ) > set_Pr1986765409at_nat ).
thf(func_def_151,type,
sK84: ( set_Pr1986765409at_nat > set_Pr1986765409at_nat ) > set_Pr1986765409at_nat ).
thf(func_def_152,type,
sK85: $o > nat > list_P559422087at_nat > nat > nat ).
thf(func_def_153,type,
sK86: $o > nat > list_P559422087at_nat > nat > nat ).
thf(func_def_154,type,
sK87: $o > nat > list_P559422087at_nat > nat > list_P559422087at_nat ).
thf(func_def_155,type,
sK88: ( nat > list_P559422087at_nat > nat > $o ) > nat ).
thf(func_def_156,type,
sK89: ( nat > list_P559422087at_nat > nat > $o ) > nat ).
thf(func_def_157,type,
sK90: ( nat > list_P559422087at_nat > nat > $o ) > nat ).
thf(func_def_158,type,
sK91: ( nat > list_P559422087at_nat > nat > $o ) > list_P559422087at_nat ).
thf(func_def_159,type,
sK92: ( nat > list_P559422087at_nat > nat > $o ) > nat ).
thf(func_def_160,type,
sK93: ( nat > list_P559422087at_nat > nat > $o ) > nat ).
thf(func_def_161,type,
sK94: ( nat > list_P559422087at_nat > nat > $o ) > nat ).
thf(func_def_162,type,
sK95: ( set_nat > set_nat ) > set_nat ).
thf(func_def_163,type,
sK96: ( set_nat > set_nat ) > set_nat ).
thf(func_def_164,type,
sK97: ( set_nat > nat ) > set_nat ).
thf(func_def_165,type,
sK98: ( set_nat > nat ) > set_nat ).
thf(func_def_166,type,
sK99: ( set_nat > set_Pr1986765409at_nat ) > set_nat ).
thf(func_def_167,type,
sK100: ( set_nat > set_Pr1986765409at_nat ) > set_nat ).
thf(func_def_168,type,
sK101: ( nat > $o ) > ( nat > $o ) > set_nat > nat ).
thf(func_def_169,type,
sK102: ( set_nat > set_nat ) > set_nat ).
thf(func_def_170,type,
sK103: ( set_nat > set_nat ) > set_nat ).
thf(func_def_171,type,
sK104: ( set_nat > nat ) > set_nat ).
thf(func_def_172,type,
sK105: ( set_nat > nat ) > set_nat ).
thf(func_def_173,type,
sK106: ( set_nat > set_Pr1986765409at_nat ) > set_nat ).
thf(func_def_174,type,
sK107: ( set_nat > set_Pr1986765409at_nat ) > set_nat ).
thf(func_def_175,type,
sK108: ( nat > set_nat ) > nat ).
thf(func_def_176,type,
sK109: ( nat > set_nat ) > nat ).
thf(func_def_177,type,
sK110: ( nat > nat ) > nat ).
thf(func_def_178,type,
sK111: ( nat > nat ) > nat ).
thf(func_def_179,type,
sK112: ( nat > set_Pr1986765409at_nat ) > nat ).
thf(func_def_180,type,
sK113: ( nat > set_Pr1986765409at_nat ) > nat ).
thf(func_def_181,type,
sK114: ( nat > set_nat ) > nat ).
thf(func_def_182,type,
sK115: ( nat > set_nat ) > nat ).
thf(func_def_183,type,
sK116: ( nat > nat ) > nat ).
thf(func_def_184,type,
sK117: ( nat > nat ) > nat ).
thf(func_def_185,type,
sK118: ( nat > set_Pr1986765409at_nat ) > nat ).
thf(func_def_186,type,
sK119: ( nat > set_Pr1986765409at_nat ) > nat ).
thf(func_def_187,type,
sK120: ( set_Pr1986765409at_nat > set_nat ) > set_Pr1986765409at_nat ).
thf(func_def_188,type,
sK121: ( set_Pr1986765409at_nat > set_nat ) > set_Pr1986765409at_nat ).
thf(func_def_189,type,
sK122: ( set_Pr1986765409at_nat > nat ) > set_Pr1986765409at_nat ).
thf(func_def_190,type,
sK123: ( set_Pr1986765409at_nat > nat ) > set_Pr1986765409at_nat ).
thf(func_def_191,type,
sK124: ( set_Pr1986765409at_nat > set_Pr1986765409at_nat ) > set_Pr1986765409at_nat ).
thf(func_def_192,type,
sK125: ( set_Pr1986765409at_nat > set_Pr1986765409at_nat ) > set_Pr1986765409at_nat ).
thf(func_def_193,type,
sK126: ( product_prod_nat_nat > $o ) > ( product_prod_nat_nat > $o ) > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_194,type,
sK127: ( set_Pr1986765409at_nat > set_nat ) > set_Pr1986765409at_nat ).
thf(func_def_195,type,
sK128: ( set_Pr1986765409at_nat > set_nat ) > set_Pr1986765409at_nat ).
thf(func_def_196,type,
sK129: ( set_Pr1986765409at_nat > nat ) > set_Pr1986765409at_nat ).
thf(func_def_197,type,
sK130: ( set_Pr1986765409at_nat > nat ) > set_Pr1986765409at_nat ).
thf(func_def_198,type,
sK131: ( set_Pr1986765409at_nat > set_Pr1986765409at_nat ) > set_Pr1986765409at_nat ).
thf(func_def_199,type,
sK132: ( set_Pr1986765409at_nat > set_Pr1986765409at_nat ) > set_Pr1986765409at_nat ).
thf(func_def_200,type,
sK133: ( set_nat > set_nat ) > set_nat ).
thf(func_def_201,type,
sK134: ( set_nat > set_nat ) > set_nat ).
thf(func_def_202,type,
sK135: ( nat > set_nat ) > nat ).
thf(func_def_203,type,
sK136: ( nat > set_nat ) > nat ).
thf(func_def_204,type,
sK137: ( set_Pr1986765409at_nat > set_nat ) > set_Pr1986765409at_nat ).
thf(func_def_205,type,
sK138: ( set_Pr1986765409at_nat > set_nat ) > set_Pr1986765409at_nat ).
thf(func_def_206,type,
sK139: ( set_nat > nat ) > set_nat ).
thf(func_def_207,type,
sK140: ( set_nat > nat ) > set_nat ).
thf(func_def_208,type,
sK141: ( nat > nat ) > nat ).
thf(func_def_209,type,
sK142: ( nat > nat ) > nat ).
thf(func_def_210,type,
sK143: ( set_Pr1986765409at_nat > nat ) > set_Pr1986765409at_nat ).
thf(func_def_211,type,
sK144: ( set_Pr1986765409at_nat > nat ) > set_Pr1986765409at_nat ).
thf(func_def_212,type,
sK145: ( set_nat > set_Pr1986765409at_nat ) > set_nat ).
thf(func_def_213,type,
sK146: ( set_nat > set_Pr1986765409at_nat ) > set_nat ).
thf(func_def_214,type,
sK147: ( nat > set_Pr1986765409at_nat ) > nat ).
thf(func_def_215,type,
sK148: ( nat > set_Pr1986765409at_nat ) > nat ).
thf(func_def_216,type,
sK149: ( set_Pr1986765409at_nat > set_Pr1986765409at_nat ) > set_Pr1986765409at_nat ).
thf(func_def_217,type,
sK150: ( set_Pr1986765409at_nat > set_Pr1986765409at_nat ) > set_Pr1986765409at_nat ).
thf(func_def_218,type,
sK151: nat > list_P559422087at_nat > nat ).
thf(func_def_219,type,
sK152: nat > list_P559422087at_nat > nat ).
thf(func_def_220,type,
sK153: nat > list_P559422087at_nat > nat ).
thf(func_def_221,type,
sK154: nat > list_P559422087at_nat > nat ).
thf(func_def_223,type,
kCOMB:
!>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).
thf(func_def_224,type,
vOR: $o > $o > $o ).
thf(func_def_225,type,
sK156: list_P559422087at_nat > nat > nat > list_P559422087at_nat ).
thf(func_def_226,type,
sK157: ( product_prod_nat_nat > $o ) > ( product_prod_nat_nat > $o ) > product_prod_nat_nat ).
thf(func_def_227,type,
sK158: ( nat > $o ) > ( nat > $o ) > nat ).
thf(func_def_228,type,
sK159: set_Pr1986765409at_nat > list_P559422087at_nat > product_prod_nat_nat ).
thf(func_def_229,type,
sK160: set_nat > list_nat > nat ).
thf(f20445,plain,
$false,
inference(avatar_sat_refutation,[],[f2737,f2741,f2773,f2778,f2783,f2787,f2799,f2804,f2808,f2812,f2816,f2820,f2824,f2852,f2862,f2866,f2870,f2880,f2885,f2889,f2893,f2897,f2901,f2916,f2934,f2940,f2944,f2948,f2952,f2960,f2969,f2975,f2979,f2989,f2993,f2997,f3001,f3005,f3017,f3025,f3029,f3047,f3053,f3059,f3063,f3087,f3091,f3101,f3107,f3113,f3120,f3124,f3128,f3136,f3142,f3146,f3150,f3154,f3159,f3171,f3175,f3179,f3185,f3189,f3195,f3201,f3207,f3211,f3215,f3219,f3226,f3230,f3234,f3238,f3242,f3246,f3250,f3254,f3263,f3267,f3271,f3275,f3279,f3283,f3287,f3291,f3295,f3299,f3303,f3369,f3384,f3388,f3392,f3396,f3418,f3422,f3426,f3430,f3434,f3438,f3442,f3478,f3482,f3486,f3490,f3494,f3498,f3502,f3506,f3510,f3514,f3518,f3522,f3526,f3618,f3622,f3626,f3630,f3634,f3638,f3700,f3704,f3709,f3713,f3766,f3770,f3774,f3786,f3790,f3794,f3798,f3812,f3817,f3834,f3838,f3842,f3846,f3851,f3970,f3980,f4012,f4016,f4021,f4025,f4029,f4063,f4067,f4206,f4214,f4296,f4309,f4314,f4319,f4324,f4328,f4388,f4392,f4396,f4465,f4469,f4473,f4477,f4481,f4485,f4489,f4493,f4497,f4501,f4506,f4510,f4514,f4741,f4745,f4788,f4834,f4855,f4867,f4871,f4875,f4879,f4911,f4971,f4975,f5021,f5176,f5181,f5192,f5197,f5202,f5207,f5211,f5215,f5219,f5223,f5288,f5292,f5296,f5375,f5379,f5383,f5387,f5391,f5395,f5399,f5403,f5407,f5411,f5415,f5419,f5423,f5427,f5431,f5435,f5439,f5443,f5447,f5451,f5455,f5459,f5463,f5932,f5937,f5941,f5945,f5949,f5953,f5957,f5961,f5965,f5969,f5973,f5977,f5981,f5985,f5989,f6000,f6004,f6008,f6012,f6016,f6020,f6049,f6125,f6130,f6134,f6144,f6150,f6164,f6173,f6177,f6193,f6197,f6207,f6211,f6215,f6219,f6260,f6264,f6268,f6296,f6300,f6304,f6312,f6324,f6328,f6332,f6336,f6340,f6344,f6358,f6390,f6398,f6402,f6406,f6415,f6433,f6437,f6441,f6445,f6449,f6453,f6457,f6461,f6465,f6469,f6473,f6477,f6481,f6485,f6489,f6493,f6497,f6501,f6505,f6761,f6765,f6775,f6779,f6783,f6787,f6791,f6795,f6799,f6803,f6807,f6811,f6821,f6825,f6829,f6833,f6837,f6841,f6951,f7021,f7025,f7069,f7073,f7105,f7113,f7117,f7156,f7164,f7172,f7190,f7208,f7212,f7223,f7279,f7283,f7301,f7310,f7314,f7338,f7342,f7346,f7350,f7388,f7392,f7417,f7421,f7425,f7429,f7454,f7476,f7486,f7497,f7502,f7506,f7532,f7537,f7541,f7545,f7596,f7600,f7604,f7608,f7612,f7616,f7656,f7660,f7664,f7668,f7672,f7676,f7680,f7684,f7688,f7692,f7696,f7700,f7704,f7708,f7973,f7977,f7981,f7985,f7989,f7993,f7997,f8121,f8129,f8133,f8137,f8141,f8145,f8149,f8153,f8157,f8161,f8165,f8317,f8389,f8398,f8402,f8406,f8410,f8414,f8418,f8422,f8426,f8430,f8550,f8554,f8558,f8562,f8622,f8626,f8630,f8978,f8982,f8986,f8990,f8994,f8998,f9002,f9006,f9010,f9032,f9193,f9217,f9221,f9225,f9229,f9233,f9237,f9241,f9245,f9249,f9253,f9257,f9261,f9265,f9269,f9273,f9277,f9506,f9510,f9514,f9518,f9522,f9526,f9557,f9586,f9626,f9630,f9634,f9640,f9644,f9779,f9791,f9795,f9799,f9825,f9829,f9833,f9837,f9841,f9845,f9849,f9853,f9859,f10042,f10046,f10050,f10056,f10067,f10071,f10145,f10149,f10153,f10157,f10161,f10165,f10493,f10515,f10519,f10523,f10527,f10715,f10720,f10764,f10768,f10798,f10802,f10806,f10810,f10814,f10818,f10827,f10901,f10905,f10947,f10961,f10987,f10991,f10995,f11000,f11005,f11010,f11302,f11320,f11340,f11344,f11349,f11356,f11360,f11364,f11368,f11372,f11376,f11866,f11870,f11875,f11879,f11883,f11887,f11891,f11923,f11933,f11937,f11945,f11949,f12039,f12074,f12230,f12237,f12241,f12245,f12249,f12324,f12330,f12444,f12448,f12452,f12769,f12774,f12806,f12817,f12821,f12827,f12831,f12835,f12887,f12928,f12932,f13058,f13064,f13071,f13080,f13132,f13136,f13140,f13144,f13148,f13152,f13156,f13160,f13164,f14028,f14032,f14036,f14040,f14044,f14083,f14087,f14468,f14472,f14537,f14542,f14546,f14702,f14706,f14710,f14758,f14762,f14766,f14770,f14774,f14778,f14782,f14786,f14790,f14795,f15652,f15898,f15902,f15906,f15910,f15914,f15918,f15922,f15947,f15951,f15955,f15959,f15963,f15967,f15971,f15975,f15979,f16006,f18357,f18361,f18497,f18501,f18505,f18509,f18513,f18517,f18521,f18525,f18529,f18533,f18537,f19186,f19191,f19195,f19199,f19203,f19207,f19211,f19682,f19686,f19690,f19904,f19908,f19912,f19916,f19920,f19924,f19928,f20208,f20276,f20280,f20284,f20289,f20301,f20305,f20309,f20313,f20317,f20321,f20325,f20329,f20333,f20337,f20341,f20345,f20349,f20435,f20443]) ).
thf(f20443,plain,
( ~ spl155_360
| ~ spl155_648 ),
inference(avatar_contradiction_clause,[],[f20442]) ).
thf(f20442,plain,
( $false
| ~ spl155_360
| ~ spl155_648 ),
inference(trivial_inequality_removal,[],[f20402]) ).
thf(f20402,plain,
( ( $true = $false )
| ~ spl155_360
| ~ spl155_648 ),
inference(superposition,[],[f20320,f7655]) ).
thf(f7655,plain,
( ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),s),p),t) )
| ~ spl155_360 ),
inference(avatar_component_clause,[],[f7653]) ).
thf(f7653,plain,
( spl155_360
<=> ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),s),p),t) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_360])]) ).
thf(f20320,plain,
( ! [X0: nat,X1: nat] : ( $false = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),p),X1) )
| ~ spl155_648 ),
inference(avatar_component_clause,[],[f20319]) ).
thf(f20319,plain,
( spl155_648
<=> ! [X0: nat,X1: nat] : ( $false = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),p),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_648])]) ).
thf(f20435,plain,
( ~ spl155_360
| ~ spl155_648 ),
inference(avatar_contradiction_clause,[],[f20434]) ).
thf(f20434,plain,
( $false
| ~ spl155_360
| ~ spl155_648 ),
inference(trivial_inequality_removal,[],[f20421]) ).
thf(f20421,plain,
( ( $true = $false )
| ~ spl155_360
| ~ spl155_648 ),
inference(superposition,[],[f7655,f20320]) ).
thf(f20349,plain,
( spl155_655
| ~ spl155_248
| ~ spl155_315 ),
inference(avatar_split_clause,[],[f7037,f7019,f6148,f20347]) ).
thf(f20347,plain,
( spl155_655
<=> ! [X2: nat,X0: set_nat,X1: set_nat] :
( ( vAPP(set_nat,nat,finite_card_nat,X0) != vAPP(set_nat,nat,finite_card_nat,X1) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X1),X0) )
| ( X0 = X1 )
| ( $true = vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,X0),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_655])]) ).
thf(f6148,plain,
( spl155_248
<=> ! [X0: set_nat,X1: nat] :
( ( $true = vAPP(set_nat,$o,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB))))),X0) )
| ( $true = vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_248])]) ).
thf(f7019,plain,
( spl155_315
<=> ! [X0: set_nat,X1: set_nat] :
( ( X0 = X1 )
| ( vAPP(set_nat,nat,finite_card_nat,X0) != vAPP(set_nat,nat,finite_card_nat,X1) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X1),X0) )
| ( $true != vAPP(set_nat,$o,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB))))),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_315])]) ).
thf(f7037,plain,
( ! [X2: nat,X0: set_nat,X1: set_nat] :
( ( vAPP(set_nat,nat,finite_card_nat,X0) != vAPP(set_nat,nat,finite_card_nat,X1) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X1),X0) )
| ( X0 = X1 )
| ( $true = vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,X0),X2) ) )
| ~ spl155_248
| ~ spl155_315 ),
inference(trivial_inequality_removal,[],[f7028]) ).
thf(f7028,plain,
( ! [X2: nat,X0: set_nat,X1: set_nat] :
( ( $true != $true )
| ( vAPP(set_nat,nat,finite_card_nat,X0) != vAPP(set_nat,nat,finite_card_nat,X1) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X1),X0) )
| ( X0 = X1 )
| ( $true = vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,X0),X2) ) )
| ~ spl155_248
| ~ spl155_315 ),
inference(superposition,[],[f7020,f6149]) ).
thf(f6149,plain,
( ! [X0: set_nat,X1: nat] :
( ( $true = vAPP(set_nat,$o,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB))))),X0) )
| ( $true = vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,X0),X1) ) )
| ~ spl155_248 ),
inference(avatar_component_clause,[],[f6148]) ).
thf(f7020,plain,
( ! [X0: set_nat,X1: set_nat] :
( ( $true != vAPP(set_nat,$o,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB))))),X0) )
| ( vAPP(set_nat,nat,finite_card_nat,X0) != vAPP(set_nat,nat,finite_card_nat,X1) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X1),X0) )
| ( X0 = X1 ) )
| ~ spl155_315 ),
inference(avatar_component_clause,[],[f7019]) ).
thf(f20345,plain,
( spl155_654
| ~ spl155_94
| ~ spl155_175 ),
inference(avatar_split_clause,[],[f4848,f4832,f3394,f20343]) ).
thf(f20343,plain,
( spl155_654
<=> ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( X0 = X1 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X1),X0) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) )
| ( $true = vAPP(nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(nat,$o),sP1,X0),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_654])]) ).
thf(f3394,plain,
( spl155_94
<=> ! [X0: set_Pr1986765409at_nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0)),X1) )
| ( $true = vAPP(nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(nat,$o),sP1,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_94])]) ).
thf(f4832,plain,
( spl155_175
<=> ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( X0 = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0)),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X1),X0) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_175])]) ).
thf(f4848,plain,
( ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( X0 = X1 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X1),X0) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) )
| ( $true = vAPP(nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(nat,$o),sP1,X0),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)) ) )
| ~ spl155_94
| ~ spl155_175 ),
inference(trivial_inequality_removal,[],[f4839]) ).
thf(f4839,plain,
( ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true != $true )
| ( X0 = X1 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X1),X0) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) )
| ( $true = vAPP(nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(nat,$o),sP1,X0),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)) ) )
| ~ spl155_94
| ~ spl155_175 ),
inference(superposition,[],[f4833,f3395]) ).
thf(f3395,plain,
( ! [X0: set_Pr1986765409at_nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0)),X1) )
| ( $true = vAPP(nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(nat,$o),sP1,X0),X1) ) )
| ~ spl155_94 ),
inference(avatar_component_clause,[],[f3394]) ).
thf(f4833,plain,
( ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0)),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)) )
| ( X0 = X1 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X1),X0) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) ) )
| ~ spl155_175 ),
inference(avatar_component_clause,[],[f4832]) ).
thf(f20341,plain,
( spl155_653
| ~ spl155_92
| ~ spl155_168 ),
inference(avatar_split_clause,[],[f4706,f4499,f3386,f20339]) ).
thf(f20339,plain,
( spl155_653
<=> ! [X2: nat,X0: set_nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_nat,nat,finite_card_nat,X0)),X1) )
| ( $true = vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X1),X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_653])]) ).
thf(f3386,plain,
( spl155_92
<=> ! [X0: set_nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_nat,nat,finite_card_nat,X0)),X1) )
| ( $true = vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_92])]) ).
thf(f4499,plain,
( spl155_168
<=> ! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X1),X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_168])]) ).
thf(f4706,plain,
( ! [X2: nat,X0: set_nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_nat,nat,finite_card_nat,X0)),X1) )
| ( $true = vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X1),X2)) ) )
| ~ spl155_92
| ~ spl155_168 ),
inference(trivial_inequality_removal,[],[f4695]) ).
thf(f4695,plain,
( ! [X2: nat,X0: set_nat,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_nat,nat,finite_card_nat,X0)),X1) )
| ( $true = vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X1),X2)) ) )
| ~ spl155_92
| ~ spl155_168 ),
inference(superposition,[],[f4500,f3387]) ).
thf(f3387,plain,
( ! [X0: set_nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_nat,nat,finite_card_nat,X0)),X1) )
| ( $true = vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,X0),X1) ) )
| ~ spl155_92 ),
inference(avatar_component_clause,[],[f3386]) ).
thf(f4500,plain,
( ! [X2: nat,X0: nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X1),X2)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),X1) ) )
| ~ spl155_168 ),
inference(avatar_component_clause,[],[f4499]) ).
thf(f20337,plain,
( spl155_652
| ~ spl155_94
| ~ spl155_168 ),
inference(avatar_split_clause,[],[f4705,f4499,f3394,f20335]) ).
thf(f20335,plain,
( spl155_652
<=> ! [X2: nat,X0: set_Pr1986765409at_nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0)),X1) )
| ( $true = vAPP(nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(nat,$o),sP1,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X1),X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_652])]) ).
thf(f4705,plain,
( ! [X2: nat,X0: set_Pr1986765409at_nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0)),X1) )
| ( $true = vAPP(nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(nat,$o),sP1,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X1),X2)) ) )
| ~ spl155_94
| ~ spl155_168 ),
inference(trivial_inequality_removal,[],[f4696]) ).
thf(f4696,plain,
( ! [X2: nat,X0: set_Pr1986765409at_nat,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0)),X1) )
| ( $true = vAPP(nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(nat,$o),sP1,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X1),X2)) ) )
| ~ spl155_94
| ~ spl155_168 ),
inference(superposition,[],[f4500,f3395]) ).
thf(f20333,plain,
( spl155_651
| ~ spl155_92
| ~ spl155_167 ),
inference(avatar_split_clause,[],[f4687,f4495,f3386,f20331]) ).
thf(f20331,plain,
( spl155_651
<=> ! [X2: nat,X0: set_nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_nat,nat,finite_card_nat,X0)),X2) )
| ( $true = vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X1),X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_651])]) ).
thf(f4495,plain,
( spl155_167
<=> ! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X1),X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_167])]) ).
thf(f4687,plain,
( ! [X2: nat,X0: set_nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_nat,nat,finite_card_nat,X0)),X2) )
| ( $true = vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X1),X2)) ) )
| ~ spl155_92
| ~ spl155_167 ),
inference(trivial_inequality_removal,[],[f4676]) ).
thf(f4676,plain,
( ! [X2: nat,X0: set_nat,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_nat,nat,finite_card_nat,X0)),X2) )
| ( $true = vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X1),X2)) ) )
| ~ spl155_92
| ~ spl155_167 ),
inference(superposition,[],[f4496,f3387]) ).
thf(f4496,plain,
( ! [X2: nat,X0: nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X1),X2)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),X2) ) )
| ~ spl155_167 ),
inference(avatar_component_clause,[],[f4495]) ).
thf(f20329,plain,
( spl155_650
| ~ spl155_94
| ~ spl155_167 ),
inference(avatar_split_clause,[],[f4686,f4495,f3394,f20327]) ).
thf(f20327,plain,
( spl155_650
<=> ! [X2: nat,X0: set_Pr1986765409at_nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0)),X2) )
| ( $true = vAPP(nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(nat,$o),sP1,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X1),X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_650])]) ).
thf(f4686,plain,
( ! [X2: nat,X0: set_Pr1986765409at_nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0)),X2) )
| ( $true = vAPP(nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(nat,$o),sP1,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X1),X2)) ) )
| ~ spl155_94
| ~ spl155_167 ),
inference(trivial_inequality_removal,[],[f4677]) ).
thf(f4677,plain,
( ! [X2: nat,X0: set_Pr1986765409at_nat,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0)),X2) )
| ( $true = vAPP(nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(nat,$o),sP1,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X1),X2)) ) )
| ~ spl155_94
| ~ spl155_167 ),
inference(superposition,[],[f4496,f3395]) ).
thf(f20325,plain,
( spl155_649
| ~ spl155_91
| ~ spl155_164 ),
inference(avatar_split_clause,[],[f4639,f4483,f3382,f20323]) ).
thf(f20323,plain,
( spl155_649
<=> ! [X2: set_Pr1986765409at_nat,X0: nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X2),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sK11,X0),X1))),X1) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_649])]) ).
thf(f3382,plain,
( spl155_91
<=> ! [X0: set_Pr1986765409at_nat,X1: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sK11,X1),X0)),X0) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_91])]) ).
thf(f4483,plain,
( spl155_164
<=> ! [X2: set_Pr1986765409at_nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X2),X0)),X1) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_164])]) ).
thf(f4639,plain,
( ! [X2: set_Pr1986765409at_nat,X0: nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X2),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sK11,X0),X1))),X1) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X1) ) )
| ~ spl155_91
| ~ spl155_164 ),
inference(trivial_inequality_removal,[],[f4618]) ).
thf(f4618,plain,
( ! [X2: set_Pr1986765409at_nat,X0: nat,X1: set_Pr1986765409at_nat] :
( ( $true != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X2),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sK11,X0),X1))),X1) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X1) ) )
| ~ spl155_91
| ~ spl155_164 ),
inference(superposition,[],[f4484,f3383]) ).
thf(f3383,plain,
( ! [X0: set_Pr1986765409at_nat,X1: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sK11,X1),X0)),X0) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) ) )
| ~ spl155_91 ),
inference(avatar_component_clause,[],[f3382]) ).
thf(f4484,plain,
( ! [X2: set_Pr1986765409at_nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X1) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X2),X0)),X1) ) )
| ~ spl155_164 ),
inference(avatar_component_clause,[],[f4483]) ).
thf(f20321,plain,
( spl155_648
| ~ spl155_622
| ~ spl155_634 ),
inference(avatar_split_clause,[],[f20270,f19914,f19188,f20319]) ).
thf(f19188,plain,
( spl155_622
<=> ( $false = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_622])]) ).
thf(f19914,plain,
( spl155_634
<=> ! [X2: nat,X0: product_prod_nat_nat > a,X1: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) )
| ( $false = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,X0),X1),p),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_634])]) ).
thf(f20270,plain,
( ! [X0: nat,X1: nat] : ( $false = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),p),X1) )
| ~ spl155_622
| ~ spl155_634 ),
inference(trivial_inequality_removal,[],[f20209]) ).
thf(f20209,plain,
( ! [X0: nat,X1: nat] :
( ( $true = $false )
| ( $false = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),p),X1) ) )
| ~ spl155_622
| ~ spl155_634 ),
inference(superposition,[],[f19915,f19190]) ).
thf(f19190,plain,
( ( $false = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) )
| ~ spl155_622 ),
inference(avatar_component_clause,[],[f19188]) ).
thf(f19915,plain,
( ! [X2: nat,X0: product_prod_nat_nat > a,X1: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) )
| ( $false = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,X0),X1),p),X2) ) )
| ~ spl155_634 ),
inference(avatar_component_clause,[],[f19914]) ).
thf(f20317,plain,
( spl155_647
| ~ spl155_91
| ~ spl155_163 ),
inference(avatar_split_clause,[],[f4611,f4479,f3382,f20315]) ).
thf(f20315,plain,
( spl155_647
<=> ! [X2: set_Pr1986765409at_nat,X0: nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sK11,X0),X1)),X2)),X1) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_647])]) ).
thf(f4479,plain,
( spl155_163
<=> ! [X2: set_Pr1986765409at_nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X2)),X1) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_163])]) ).
thf(f4611,plain,
( ! [X2: set_Pr1986765409at_nat,X0: nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sK11,X0),X1)),X2)),X1) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X1) ) )
| ~ spl155_91
| ~ spl155_163 ),
inference(trivial_inequality_removal,[],[f4590]) ).
thf(f4590,plain,
( ! [X2: set_Pr1986765409at_nat,X0: nat,X1: set_Pr1986765409at_nat] :
( ( $true != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sK11,X0),X1)),X2)),X1) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X1) ) )
| ~ spl155_91
| ~ spl155_163 ),
inference(superposition,[],[f4480,f3383]) ).
thf(f4480,plain,
( ! [X2: set_Pr1986765409at_nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X1) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X2)),X1) ) )
| ~ spl155_163 ),
inference(avatar_component_clause,[],[f4479]) ).
thf(f20313,plain,
( spl155_646
| ~ spl155_92
| ~ spl155_162 ),
inference(avatar_split_clause,[],[f4583,f4475,f3386,f20311]) ).
thf(f20311,plain,
( spl155_646
<=> ! [X2: nat,X0: set_nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,vAPP(set_nat,nat,finite_card_nat,X0)),X2)),X1) )
| ( $true = vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_646])]) ).
thf(f4475,plain,
( spl155_162
<=> ! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X2)),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_162])]) ).
thf(f4583,plain,
( ! [X2: nat,X0: set_nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,vAPP(set_nat,nat,finite_card_nat,X0)),X2)),X1) )
| ( $true = vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,X0),X1) ) )
| ~ spl155_92
| ~ spl155_162 ),
inference(trivial_inequality_removal,[],[f4568]) ).
thf(f4568,plain,
( ! [X2: nat,X0: set_nat,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,vAPP(set_nat,nat,finite_card_nat,X0)),X2)),X1) )
| ( $true = vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,X0),X1) ) )
| ~ spl155_92
| ~ spl155_162 ),
inference(superposition,[],[f4476,f3387]) ).
thf(f4476,plain,
( ! [X2: nat,X0: nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),X1) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X2)),X1) ) )
| ~ spl155_162 ),
inference(avatar_component_clause,[],[f4475]) ).
thf(f20309,plain,
( spl155_645
| ~ spl155_94
| ~ spl155_162 ),
inference(avatar_split_clause,[],[f4582,f4475,f3394,f20307]) ).
thf(f20307,plain,
( spl155_645
<=> ! [X2: nat,X0: set_Pr1986765409at_nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0)),X2)),X1) )
| ( $true = vAPP(nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(nat,$o),sP1,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_645])]) ).
thf(f4582,plain,
( ! [X2: nat,X0: set_Pr1986765409at_nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0)),X2)),X1) )
| ( $true = vAPP(nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(nat,$o),sP1,X0),X1) ) )
| ~ spl155_94
| ~ spl155_162 ),
inference(trivial_inequality_removal,[],[f4569]) ).
thf(f4569,plain,
( ! [X2: nat,X0: set_Pr1986765409at_nat,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0)),X2)),X1) )
| ( $true = vAPP(nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(nat,$o),sP1,X0),X1) ) )
| ~ spl155_94
| ~ spl155_162 ),
inference(superposition,[],[f4476,f3395]) ).
thf(f20305,plain,
( spl155_644
| ~ spl155_92
| ~ spl155_161 ),
inference(avatar_split_clause,[],[f4561,f4471,f3386,f20303]) ).
thf(f20303,plain,
( spl155_644
<=> ! [X2: nat,X0: set_nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X2),vAPP(set_nat,nat,finite_card_nat,X0))),X1) )
| ( $true = vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_644])]) ).
thf(f4471,plain,
( spl155_161
<=> ! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X2),X0)),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_161])]) ).
thf(f4561,plain,
( ! [X2: nat,X0: set_nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X2),vAPP(set_nat,nat,finite_card_nat,X0))),X1) )
| ( $true = vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,X0),X1) ) )
| ~ spl155_92
| ~ spl155_161 ),
inference(trivial_inequality_removal,[],[f4546]) ).
thf(f4546,plain,
( ! [X2: nat,X0: set_nat,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X2),vAPP(set_nat,nat,finite_card_nat,X0))),X1) )
| ( $true = vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,X0),X1) ) )
| ~ spl155_92
| ~ spl155_161 ),
inference(superposition,[],[f4472,f3387]) ).
thf(f4472,plain,
( ! [X2: nat,X0: nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),X1) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X2),X0)),X1) ) )
| ~ spl155_161 ),
inference(avatar_component_clause,[],[f4471]) ).
thf(f20301,plain,
( spl155_643
| ~ spl155_94
| ~ spl155_161 ),
inference(avatar_split_clause,[],[f4560,f4471,f3394,f20299]) ).
thf(f20299,plain,
( spl155_643
<=> ! [X2: nat,X0: set_Pr1986765409at_nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X2),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0))),X1) )
| ( $true = vAPP(nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(nat,$o),sP1,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_643])]) ).
thf(f4560,plain,
( ! [X2: nat,X0: set_Pr1986765409at_nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X2),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0))),X1) )
| ( $true = vAPP(nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(nat,$o),sP1,X0),X1) ) )
| ~ spl155_94
| ~ spl155_161 ),
inference(trivial_inequality_removal,[],[f4547]) ).
thf(f4547,plain,
( ! [X2: nat,X0: set_Pr1986765409at_nat,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X2),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0))),X1) )
| ( $true = vAPP(nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(nat,$o),sP1,X0),X1) ) )
| ~ spl155_94
| ~ spl155_161 ),
inference(superposition,[],[f4472,f3395]) ).
thf(f20289,plain,
( ~ spl155_642
| spl155_394
| ~ spl155_79
| ~ spl155_158 ),
inference(avatar_split_clause,[],[f4450,f4394,f3260,f8391,f20286]) ).
thf(f20286,plain,
( spl155_642
<=> ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,c)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_642])]) ).
thf(f8391,plain,
( spl155_394
<=> ( vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c) = vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,c) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_394])]) ).
thf(f3260,plain,
( spl155_79
<=> ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,c)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_79])]) ).
thf(f4394,plain,
( spl155_158
<=> ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( X0 = X1 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X1),X0) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_158])]) ).
thf(f4450,plain,
( ( vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c) = vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,c) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,c)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) )
| ~ spl155_79
| ~ spl155_158 ),
inference(trivial_inequality_removal,[],[f4435]) ).
thf(f4435,plain,
( ( $true != $true )
| ( vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c) = vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,c) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,c)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) )
| ~ spl155_79
| ~ spl155_158 ),
inference(superposition,[],[f4395,f3262]) ).
thf(f3262,plain,
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,c)) )
| ~ spl155_79 ),
inference(avatar_component_clause,[],[f3260]) ).
thf(f4395,plain,
( ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X1),X0) )
| ( X0 = X1 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X1) ) )
| ~ spl155_158 ),
inference(avatar_component_clause,[],[f4394]) ).
thf(f20284,plain,
( spl155_641
| ~ spl155_126
| ~ spl155_155 ),
inference(avatar_split_clause,[],[f4383,f4326,f3768,f20282]) ).
thf(f20282,plain,
( spl155_641
<=> ! [X0: set_nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,X0),X1) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X1),vAPP(set_nat,nat,finite_card_nat,vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK14,X0),X1))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_641])]) ).
thf(f3768,plain,
( spl155_126
<=> ! [X0: nat,X1: set_nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_nat,nat,finite_card_nat,vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK14,X1),X0))),X0) )
| ( $true != vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_126])]) ).
thf(f4326,plain,
( spl155_155
<=> ! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X1),X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_155])]) ).
thf(f4383,plain,
( ! [X0: set_nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,X0),X1) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X1),vAPP(set_nat,nat,finite_card_nat,vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK14,X0),X1))) ) )
| ~ spl155_126
| ~ spl155_155 ),
inference(trivial_inequality_removal,[],[f4330]) ).
thf(f4330,plain,
( ! [X0: set_nat,X1: nat] :
( ( $true != $true )
| ( $true != vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,X0),X1) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X1),vAPP(set_nat,nat,finite_card_nat,vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK14,X0),X1))) ) )
| ~ spl155_126
| ~ spl155_155 ),
inference(superposition,[],[f3769,f4327]) ).
thf(f4327,plain,
( ! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X1),X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),X1) ) )
| ~ spl155_155 ),
inference(avatar_component_clause,[],[f4326]) ).
thf(f3769,plain,
( ! [X0: nat,X1: set_nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_nat,nat,finite_card_nat,vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK14,X1),X0))),X0) )
| ( $true != vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,X1),X0) ) )
| ~ spl155_126 ),
inference(avatar_component_clause,[],[f3768]) ).
thf(f20280,plain,
( spl155_640
| ~ spl155_127
| ~ spl155_155 ),
inference(avatar_split_clause,[],[f4382,f4326,f3772,f20278]) ).
thf(f20278,plain,
( spl155_640
<=> ! [X0: set_Pr1986765409at_nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(nat,$o),sP1,X0),X1) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X1),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK17,X0),X1))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_640])]) ).
thf(f3772,plain,
( spl155_127
<=> ! [X0: nat,X1: set_Pr1986765409at_nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK17,X1),X0))),X0) )
| ( $true != vAPP(nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(nat,$o),sP1,X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_127])]) ).
thf(f4382,plain,
( ! [X0: set_Pr1986765409at_nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(nat,$o),sP1,X0),X1) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X1),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK17,X0),X1))) ) )
| ~ spl155_127
| ~ spl155_155 ),
inference(trivial_inequality_removal,[],[f4331]) ).
thf(f4331,plain,
( ! [X0: set_Pr1986765409at_nat,X1: nat] :
( ( $true != $true )
| ( $true != vAPP(nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(nat,$o),sP1,X0),X1) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X1),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK17,X0),X1))) ) )
| ~ spl155_127
| ~ spl155_155 ),
inference(superposition,[],[f3773,f4327]) ).
thf(f3773,plain,
( ! [X0: nat,X1: set_Pr1986765409at_nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK17,X1),X0))),X0) )
| ( $true != vAPP(nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(nat,$o),sP1,X1),X0) ) )
| ~ spl155_127 ),
inference(avatar_component_clause,[],[f3772]) ).
thf(f20276,plain,
( spl155_639
| ~ spl155_2
| ~ spl155_127 ),
inference(avatar_split_clause,[],[f3781,f3772,f2739,f20274]) ).
thf(f20274,plain,
( spl155_639
<=> ! [X0: set_Pr1986765409at_nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(nat,$o),sP1,X0),X1) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK17,X0),X1))),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_639])]) ).
thf(f2739,plain,
( spl155_2
<=> ! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_2])]) ).
thf(f3781,plain,
( ! [X0: set_Pr1986765409at_nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(nat,$o),sP1,X0),X1) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK17,X0),X1))),X1) ) )
| ~ spl155_2
| ~ spl155_127 ),
inference(trivial_inequality_removal,[],[f3780]) ).
thf(f3780,plain,
( ! [X0: set_Pr1986765409at_nat,X1: nat] :
( ( $true != $true )
| ( $true != vAPP(nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(nat,$o),sP1,X0),X1) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK17,X0),X1))),X1) ) )
| ~ spl155_2
| ~ spl155_127 ),
inference(superposition,[],[f3773,f2740]) ).
thf(f2740,plain,
( ! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) )
| ~ spl155_2 ),
inference(avatar_component_clause,[],[f2739]) ).
thf(f20208,plain,
( spl155_638
| ~ spl155_2
| ~ spl155_126 ),
inference(avatar_split_clause,[],[f3777,f3768,f2739,f20206]) ).
thf(f20206,plain,
( spl155_638
<=> ! [X0: set_nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,X0),X1) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_nat,nat,finite_card_nat,vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK14,X0),X1))),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_638])]) ).
thf(f3777,plain,
( ! [X0: set_nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,X0),X1) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_nat,nat,finite_card_nat,vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK14,X0),X1))),X1) ) )
| ~ spl155_2
| ~ spl155_126 ),
inference(trivial_inequality_removal,[],[f3776]) ).
thf(f3776,plain,
( ! [X0: set_nat,X1: nat] :
( ( $true != $true )
| ( $true != vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,X0),X1) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_nat,nat,finite_card_nat,vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK14,X0),X1))),X1) ) )
| ~ spl155_2
| ~ spl155_126 ),
inference(superposition,[],[f3769,f2740]) ).
thf(f19928,plain,
( spl155_637
| ~ spl155_258
| ~ spl155_322 ),
inference(avatar_split_clause,[],[f7160,f7154,f6257,f19926]) ).
thf(f19926,plain,
( spl155_637
<=> ! [X0: nat,X1: nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,c),X0),X1)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_637])]) ).
thf(f6257,plain,
( spl155_258
<=> ( $true = vAPP(sTfun(product_prod_nat_nat,a),$o,vAPP(sTfun(sTfun(product_prod_nat_nat,a),set_nat),sTfun(sTfun(product_prod_nat_nat,a),$o),vAPP(sTfun(set_nat,$o),sTfun(sTfun(sTfun(product_prod_nat_nat,a),set_nat),sTfun(sTfun(product_prod_nat_nat,a),$o)),bCOMB,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB)))))),v_a),c) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_258])]) ).
thf(f7154,plain,
( spl155_322
<=> ! [X2: nat,X0: product_prod_nat_nat > a,X1: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,X0),X1),X2)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) )
| ( $true != vAPP(sTfun(product_prod_nat_nat,a),$o,vAPP(sTfun(sTfun(product_prod_nat_nat,a),set_nat),sTfun(sTfun(product_prod_nat_nat,a),$o),vAPP(sTfun(set_nat,$o),sTfun(sTfun(sTfun(product_prod_nat_nat,a),set_nat),sTfun(sTfun(product_prod_nat_nat,a),$o)),bCOMB,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB)))))),v_a),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_322])]) ).
thf(f7160,plain,
( ! [X0: nat,X1: nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,c),X0),X1)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) )
| ~ spl155_258
| ~ spl155_322 ),
inference(trivial_inequality_removal,[],[f7157]) ).
thf(f7157,plain,
( ! [X0: nat,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,c),X0),X1)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) ) )
| ~ spl155_258
| ~ spl155_322 ),
inference(superposition,[],[f7155,f6259]) ).
thf(f6259,plain,
( ( $true = vAPP(sTfun(product_prod_nat_nat,a),$o,vAPP(sTfun(sTfun(product_prod_nat_nat,a),set_nat),sTfun(sTfun(product_prod_nat_nat,a),$o),vAPP(sTfun(set_nat,$o),sTfun(sTfun(sTfun(product_prod_nat_nat,a),set_nat),sTfun(sTfun(product_prod_nat_nat,a),$o)),bCOMB,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB)))))),v_a),c) )
| ~ spl155_258 ),
inference(avatar_component_clause,[],[f6257]) ).
thf(f7155,plain,
( ! [X2: nat,X0: product_prod_nat_nat > a,X1: nat] :
( ( $true != vAPP(sTfun(product_prod_nat_nat,a),$o,vAPP(sTfun(sTfun(product_prod_nat_nat,a),set_nat),sTfun(sTfun(product_prod_nat_nat,a),$o),vAPP(sTfun(set_nat,$o),sTfun(sTfun(sTfun(product_prod_nat_nat,a),set_nat),sTfun(sTfun(product_prod_nat_nat,a),$o)),bCOMB,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB)))))),v_a),X0) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,X0),X1),X2)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) ) )
| ~ spl155_322 ),
inference(avatar_component_clause,[],[f7154]) ).
thf(f19924,plain,
( spl155_636
| ~ spl155_244
| ~ spl155_315 ),
inference(avatar_split_clause,[],[f7035,f7019,f6123,f19922]) ).
thf(f19922,plain,
( spl155_636
<=> ! [X0: list_nat,X1: set_nat] :
( ( vAPP(set_nat,nat,finite_card_nat,X1) != vAPP(set_nat,nat,finite_card_nat,vAPP(list_nat,set_nat,set_nat2,X0)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X1),vAPP(list_nat,set_nat,set_nat2,X0)) )
| ( vAPP(list_nat,set_nat,set_nat2,X0) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_636])]) ).
thf(f6123,plain,
( spl155_244
<=> ! [X0: list_nat] : ( $true = vAPP(set_nat,$o,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB))))),vAPP(list_nat,set_nat,set_nat2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_244])]) ).
thf(f7035,plain,
( ! [X0: list_nat,X1: set_nat] :
( ( vAPP(set_nat,nat,finite_card_nat,X1) != vAPP(set_nat,nat,finite_card_nat,vAPP(list_nat,set_nat,set_nat2,X0)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X1),vAPP(list_nat,set_nat,set_nat2,X0)) )
| ( vAPP(list_nat,set_nat,set_nat2,X0) = X1 ) )
| ~ spl155_244
| ~ spl155_315 ),
inference(trivial_inequality_removal,[],[f7030]) ).
thf(f7030,plain,
( ! [X0: list_nat,X1: set_nat] :
( ( $true != $true )
| ( vAPP(set_nat,nat,finite_card_nat,X1) != vAPP(set_nat,nat,finite_card_nat,vAPP(list_nat,set_nat,set_nat2,X0)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X1),vAPP(list_nat,set_nat,set_nat2,X0)) )
| ( vAPP(list_nat,set_nat,set_nat2,X0) = X1 ) )
| ~ spl155_244
| ~ spl155_315 ),
inference(superposition,[],[f7020,f6124]) ).
thf(f6124,plain,
( ! [X0: list_nat] : ( $true = vAPP(set_nat,$o,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB))))),vAPP(list_nat,set_nat,set_nat2,X0)) )
| ~ spl155_244 ),
inference(avatar_component_clause,[],[f6123]) ).
thf(f19920,plain,
( spl155_635
| ~ spl155_119
| ~ spl155_158 ),
inference(avatar_split_clause,[],[f4452,f4394,f3632,f19918]) ).
thf(f19918,plain,
( spl155_635
<=> ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( X0 = X1 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X1),X0) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,X1),X0)),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_635])]) ).
thf(f3632,plain,
( spl155_119
<=> ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X1) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,X1),X0)),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_119])]) ).
thf(f4452,plain,
( ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( X0 = X1 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X1),X0) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,X1),X0)),X0) ) )
| ~ spl155_119
| ~ spl155_158 ),
inference(trivial_inequality_removal,[],[f4433]) ).
thf(f4433,plain,
( ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true != $true )
| ( X0 = X1 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X1),X0) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,X1),X0)),X0) ) )
| ~ spl155_119
| ~ spl155_158 ),
inference(superposition,[],[f4395,f3633]) ).
thf(f3633,plain,
( ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X1) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,X1),X0)),X0) ) )
| ~ spl155_119 ),
inference(avatar_component_clause,[],[f3632]) ).
thf(f19916,plain,
( spl155_634
| ~ spl155_354
| ~ spl155_498 ),
inference(avatar_split_clause,[],[f10983,f10959,f7593,f19914]) ).
thf(f7593,plain,
( spl155_354
<=> ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_354])]) ).
thf(f10959,plain,
( spl155_498
<=> ! [X4: product_prod_nat_nat,X0: product_prod_nat_nat > a,X3: nat,X2: list_P559422087at_nat,X1: nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X4),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X2)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X4),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) )
| ( $false = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,X0),X1),X2),X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_498])]) ).
thf(f10983,plain,
( ! [X2: nat,X0: product_prod_nat_nat > a,X1: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) )
| ( $false = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,X0),X1),p),X2) ) )
| ~ spl155_354
| ~ spl155_498 ),
inference(trivial_inequality_removal,[],[f10968]) ).
thf(f10968,plain,
( ! [X2: nat,X0: product_prod_nat_nat > a,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) )
| ( $false = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,X0),X1),p),X2) ) )
| ~ spl155_354
| ~ spl155_498 ),
inference(superposition,[],[f10960,f7595]) ).
thf(f7595,plain,
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p)) )
| ~ spl155_354 ),
inference(avatar_component_clause,[],[f7593]) ).
thf(f10960,plain,
( ! [X2: list_P559422087at_nat,X3: nat,X0: product_prod_nat_nat > a,X1: nat,X4: product_prod_nat_nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X4),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X2)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X4),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) )
| ( $false = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,X0),X1),X2),X3) ) )
| ~ spl155_498 ),
inference(avatar_component_clause,[],[f10959]) ).
thf(f19912,plain,
( spl155_633
| ~ spl155_117
| ~ spl155_156 ),
inference(avatar_split_clause,[],[f4407,f4386,f3624,f19910]) ).
thf(f19910,plain,
( spl155_633
<=> ! [X0: set_nat,X1: set_nat] :
( ( X0 = X1 )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X1),X0) )
| ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,vAPP(set_nat,nat,vAPP(set_nat,sTfun(set_nat,nat),sK15,X1),X0)),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_633])]) ).
thf(f3624,plain,
( spl155_117
<=> ! [X0: set_nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),X1) )
| ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,vAPP(set_nat,nat,vAPP(set_nat,sTfun(set_nat,nat),sK15,X1),X0)),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_117])]) ).
thf(f4386,plain,
( spl155_156
<=> ! [X0: set_nat,X1: set_nat] :
( ( X0 = X1 )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X1),X0) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_156])]) ).
thf(f4407,plain,
( ! [X0: set_nat,X1: set_nat] :
( ( X0 = X1 )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X1),X0) )
| ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,vAPP(set_nat,nat,vAPP(set_nat,sTfun(set_nat,nat),sK15,X1),X0)),X0) ) )
| ~ spl155_117
| ~ spl155_156 ),
inference(trivial_inequality_removal,[],[f4400]) ).
thf(f4400,plain,
( ! [X0: set_nat,X1: set_nat] :
( ( $true != $true )
| ( X0 = X1 )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X1),X0) )
| ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,vAPP(set_nat,nat,vAPP(set_nat,sTfun(set_nat,nat),sK15,X1),X0)),X0) ) )
| ~ spl155_117
| ~ spl155_156 ),
inference(superposition,[],[f4387,f3625]) ).
thf(f3625,plain,
( ! [X0: set_nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),X1) )
| ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,vAPP(set_nat,nat,vAPP(set_nat,sTfun(set_nat,nat),sK15,X1),X0)),X0) ) )
| ~ spl155_117 ),
inference(avatar_component_clause,[],[f3624]) ).
thf(f4387,plain,
( ! [X0: set_nat,X1: set_nat] :
( ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X1),X0) )
| ( X0 = X1 )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),X1) ) )
| ~ spl155_156 ),
inference(avatar_component_clause,[],[f4386]) ).
thf(f19908,plain,
( spl155_632
| ~ spl155_2
| ~ spl155_122 ),
inference(avatar_split_clause,[],[f3737,f3702,f2739,f19906]) ).
thf(f19906,plain,
( spl155_632
<=> ! [X2: product_prod_nat_nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X2),X0) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X2),X1) )
| ( $false = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_632])]) ).
thf(f3702,plain,
( spl155_122
<=> ! [X2: product_prod_nat_nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X2),X1) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X2),X0) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_122])]) ).
thf(f3737,plain,
( ! [X2: product_prod_nat_nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X2),X0) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X2),X1) )
| ( $false = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X1) ) )
| ~ spl155_2
| ~ spl155_122 ),
inference(trivial_inequality_removal,[],[f3736]) ).
thf(f3736,plain,
( ! [X2: product_prod_nat_nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true != $true )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X2),X0) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X2),X1) )
| ( $false = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X1) ) )
| ~ spl155_2
| ~ spl155_122 ),
inference(superposition,[],[f3703,f2740]) ).
thf(f3703,plain,
( ! [X2: product_prod_nat_nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X1) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X2),X0) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X2),X1) ) )
| ~ spl155_122 ),
inference(avatar_component_clause,[],[f3702]) ).
thf(f19904,plain,
( spl155_631
| ~ spl155_2
| ~ spl155_121 ),
inference(avatar_split_clause,[],[f3720,f3698,f2739,f19902]) ).
thf(f19902,plain,
( spl155_631
<=> ! [X2: nat,X0: set_nat,X1: set_nat] :
( ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X2),X0) )
| ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X2),X1) )
| ( $false = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_631])]) ).
thf(f3698,plain,
( spl155_121
<=> ! [X2: nat,X0: set_nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X2),X1) )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X2),X0) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_121])]) ).
thf(f3720,plain,
( ! [X2: nat,X0: set_nat,X1: set_nat] :
( ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X2),X0) )
| ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X2),X1) )
| ( $false = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),X1) ) )
| ~ spl155_2
| ~ spl155_121 ),
inference(trivial_inequality_removal,[],[f3719]) ).
thf(f3719,plain,
( ! [X2: nat,X0: set_nat,X1: set_nat] :
( ( $true != $true )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X2),X0) )
| ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X2),X1) )
| ( $false = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),X1) ) )
| ~ spl155_2
| ~ spl155_121 ),
inference(superposition,[],[f3699,f2740]) ).
thf(f3699,plain,
( ! [X2: nat,X0: set_nat,X1: set_nat] :
( ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),X1) )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X2),X0) )
| ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X2),X1) ) )
| ~ spl155_121 ),
inference(avatar_component_clause,[],[f3698]) ).
thf(f19690,plain,
( spl155_630
| ~ spl155_76
| ~ spl155_174 ),
inference(avatar_split_clause,[],[f4814,f4786,f3244,f19688]) ).
thf(f19688,plain,
( spl155_630
<=> ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1))),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_630])]) ).
thf(f3244,plain,
( spl155_76
<=> ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_76])]) ).
thf(f4786,plain,
( spl155_174
<=> ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X1),X0) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_174])]) ).
thf(f4814,plain,
( ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1))),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) ) )
| ~ spl155_76
| ~ spl155_174 ),
inference(trivial_inequality_removal,[],[f4790]) ).
thf(f4790,plain,
( ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true != $true )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1))),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) ) )
| ~ spl155_76
| ~ spl155_174 ),
inference(superposition,[],[f4787,f3245]) ).
thf(f3245,plain,
( ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1)),X0) )
| ~ spl155_76 ),
inference(avatar_component_clause,[],[f3244]) ).
thf(f4787,plain,
( ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X1),X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) ) )
| ~ spl155_174 ),
inference(avatar_component_clause,[],[f4786]) ).
thf(f19686,plain,
( spl155_629
| ~ spl155_77
| ~ spl155_174 ),
inference(avatar_split_clause,[],[f4813,f4786,f3248,f19684]) ).
thf(f19684,plain,
( spl155_629
<=> ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1))),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_629])]) ).
thf(f3248,plain,
( spl155_77
<=> ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_77])]) ).
thf(f4813,plain,
( ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1))),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X1) ) )
| ~ spl155_77
| ~ spl155_174 ),
inference(trivial_inequality_removal,[],[f4791]) ).
thf(f4791,plain,
( ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true != $true )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1))),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X1) ) )
| ~ spl155_77
| ~ spl155_174 ),
inference(superposition,[],[f4787,f3249]) ).
thf(f3249,plain,
( ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1)),X1) )
| ~ spl155_77 ),
inference(avatar_component_clause,[],[f3248]) ).
thf(f19682,plain,
( spl155_628
| ~ spl155_9
| ~ spl155_136 ),
inference(avatar_split_clause,[],[f3887,f3840,f2806,f19680]) ).
thf(f19680,plain,
( spl155_628
<=> ! [X0: set_Pr1986765409at_nat,X1: nat > $o] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(sTfun(nat,$o),set_nat,collect_nat,X1)),vAPP(sTfun(nat,$o),set_nat,collect_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,$o),sP1,X0))) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_628])]) ).
thf(f2806,plain,
( spl155_9
<=> ! [X0: set_Pr1986765409at_nat,X1: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) )
| ( $true = vAPP(nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(nat,$o),sP1,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_9])]) ).
thf(f3840,plain,
( spl155_136
<=> ! [X0: nat > $o,X1: nat > $o] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(sTfun(nat,$o),set_nat,collect_nat,X0)),vAPP(sTfun(nat,$o),set_nat,collect_nat,X1)) )
| ( $true != vAPP(nat,$o,X1,vAPP(sTfun(nat,$o),nat,vAPP(sTfun(nat,$o),sTfun(sTfun(nat,$o),nat),sK13,X1),X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_136])]) ).
thf(f3887,plain,
( ! [X0: set_Pr1986765409at_nat,X1: nat > $o] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(sTfun(nat,$o),set_nat,collect_nat,X1)),vAPP(sTfun(nat,$o),set_nat,collect_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,$o),sP1,X0))) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) ) )
| ~ spl155_9
| ~ spl155_136 ),
inference(trivial_inequality_removal,[],[f3880]) ).
thf(f3880,plain,
( ! [X0: set_Pr1986765409at_nat,X1: nat > $o] :
( ( $true != $true )
| ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(sTfun(nat,$o),set_nat,collect_nat,X1)),vAPP(sTfun(nat,$o),set_nat,collect_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,$o),sP1,X0))) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) ) )
| ~ spl155_9
| ~ spl155_136 ),
inference(superposition,[],[f3841,f2807]) ).
thf(f2807,plain,
( ! [X0: set_Pr1986765409at_nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(nat,$o),sP1,X0),X1) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) ) )
| ~ spl155_9 ),
inference(avatar_component_clause,[],[f2806]) ).
thf(f3841,plain,
( ! [X0: nat > $o,X1: nat > $o] :
( ( $true != vAPP(nat,$o,X1,vAPP(sTfun(nat,$o),nat,vAPP(sTfun(nat,$o),sTfun(sTfun(nat,$o),nat),sK13,X1),X0)) )
| ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(sTfun(nat,$o),set_nat,collect_nat,X0)),vAPP(sTfun(nat,$o),set_nat,collect_nat,X1)) ) )
| ~ spl155_136 ),
inference(avatar_component_clause,[],[f3840]) ).
thf(f19211,plain,
( spl155_627
| ~ spl155_75
| ~ spl155_173 ),
inference(avatar_split_clause,[],[f4782,f4743,f3240,f19209]) ).
thf(f19209,plain,
( spl155_627
<=> ! [X0: set_Pr1986765409at_nat,X1: nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK28,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0)),X1))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_627])]) ).
thf(f3240,plain,
( spl155_75
<=> ! [X0: nat,X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X1)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_75])]) ).
thf(f4743,plain,
( spl155_173
<=> ! [X0: nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK28,X1),X0)),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_173])]) ).
thf(f4782,plain,
( ! [X0: set_Pr1986765409at_nat,X1: nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK28,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0)),X1))),X0) )
| ~ spl155_75
| ~ spl155_173 ),
inference(trivial_inequality_removal,[],[f4767]) ).
thf(f4767,plain,
( ! [X0: set_Pr1986765409at_nat,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK28,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0)),X1))),X0) ) )
| ~ spl155_75
| ~ spl155_173 ),
inference(superposition,[],[f4744,f3241]) ).
thf(f3241,plain,
( ! [X0: nat,X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X1)),X0) )
| ~ spl155_75 ),
inference(avatar_component_clause,[],[f3240]) ).
thf(f4744,plain,
( ! [X0: nat,X1: set_Pr1986765409at_nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK28,X1),X0)),X1) ) )
| ~ spl155_173 ),
inference(avatar_component_clause,[],[f4743]) ).
thf(f19207,plain,
( spl155_626
| ~ spl155_74
| ~ spl155_173 ),
inference(avatar_split_clause,[],[f4781,f4743,f3236,f19205]) ).
thf(f19205,plain,
( spl155_626
<=> ! [X0: nat,X1: set_Pr1986765409at_nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK28,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_626])]) ).
thf(f3236,plain,
( spl155_74
<=> ! [X0: nat,X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_74])]) ).
thf(f4781,plain,
( ! [X0: nat,X1: set_Pr1986765409at_nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK28,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)))),X1) )
| ~ spl155_74
| ~ spl155_173 ),
inference(trivial_inequality_removal,[],[f4768]) ).
thf(f4768,plain,
( ! [X0: nat,X1: set_Pr1986765409at_nat] :
( ( $true != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK28,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)))),X1) ) )
| ~ spl155_74
| ~ spl155_173 ),
inference(superposition,[],[f4744,f3237]) ).
thf(f3237,plain,
( ! [X0: nat,X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X1)),X1) )
| ~ spl155_74 ),
inference(avatar_component_clause,[],[f3236]) ).
thf(f19203,plain,
( spl155_625
| ~ spl155_75
| ~ spl155_172 ),
inference(avatar_split_clause,[],[f4762,f4739,f3240,f19201]) ).
thf(f19201,plain,
( spl155_625
<=> ! [X0: set_nat,X1: nat] : ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK27,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,vAPP(set_nat,nat,finite_card_nat,X0)),X1))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_625])]) ).
thf(f4739,plain,
( spl155_172
<=> ! [X0: nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK27,X1),X0)),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),vAPP(set_nat,nat,finite_card_nat,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_172])]) ).
thf(f4762,plain,
( ! [X0: set_nat,X1: nat] : ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK27,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,vAPP(set_nat,nat,finite_card_nat,X0)),X1))),X0) )
| ~ spl155_75
| ~ spl155_172 ),
inference(trivial_inequality_removal,[],[f4747]) ).
thf(f4747,plain,
( ! [X0: set_nat,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK27,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,vAPP(set_nat,nat,finite_card_nat,X0)),X1))),X0) ) )
| ~ spl155_75
| ~ spl155_172 ),
inference(superposition,[],[f4740,f3241]) ).
thf(f4740,plain,
( ! [X0: nat,X1: set_nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),vAPP(set_nat,nat,finite_card_nat,X1)) )
| ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK27,X1),X0)),X1) ) )
| ~ spl155_172 ),
inference(avatar_component_clause,[],[f4739]) ).
thf(f19199,plain,
( spl155_624
| ~ spl155_74
| ~ spl155_172 ),
inference(avatar_split_clause,[],[f4761,f4739,f3236,f19197]) ).
thf(f19197,plain,
( spl155_624
<=> ! [X0: nat,X1: set_nat] : ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK27,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),vAPP(set_nat,nat,finite_card_nat,X1)))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_624])]) ).
thf(f4761,plain,
( ! [X0: nat,X1: set_nat] : ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK27,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),vAPP(set_nat,nat,finite_card_nat,X1)))),X1) )
| ~ spl155_74
| ~ spl155_172 ),
inference(trivial_inequality_removal,[],[f4748]) ).
thf(f4748,plain,
( ! [X0: nat,X1: set_nat] :
( ( $true != $true )
| ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK27,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),vAPP(set_nat,nat,finite_card_nat,X1)))),X1) ) )
| ~ spl155_74
| ~ spl155_172 ),
inference(superposition,[],[f4740,f3237]) ).
thf(f19195,plain,
( spl155_623
| ~ spl155_92
| ~ spl155_157 ),
inference(avatar_split_clause,[],[f4426,f4390,f3386,f19193]) ).
thf(f19193,plain,
( spl155_623
<=> ! [X0: set_nat,X1: nat] :
( ( vAPP(set_nat,nat,finite_card_nat,X0) = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X1),vAPP(set_nat,nat,finite_card_nat,X0)) )
| ( $true = vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_623])]) ).
thf(f4390,plain,
( spl155_157
<=> ! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X1),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_157])]) ).
thf(f4426,plain,
( ! [X0: set_nat,X1: nat] :
( ( vAPP(set_nat,nat,finite_card_nat,X0) = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X1),vAPP(set_nat,nat,finite_card_nat,X0)) )
| ( $true = vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,X0),X1) ) )
| ~ spl155_92
| ~ spl155_157 ),
inference(trivial_inequality_removal,[],[f4413]) ).
thf(f4413,plain,
( ! [X0: set_nat,X1: nat] :
( ( $true != $true )
| ( vAPP(set_nat,nat,finite_card_nat,X0) = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X1),vAPP(set_nat,nat,finite_card_nat,X0)) )
| ( $true = vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,X0),X1) ) )
| ~ spl155_92
| ~ spl155_157 ),
inference(superposition,[],[f4391,f3387]) ).
thf(f4391,plain,
( ! [X0: nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X1),X0) )
| ( X0 = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),X1) ) )
| ~ spl155_157 ),
inference(avatar_component_clause,[],[f4390]) ).
thf(f19191,plain,
( spl155_622
| ~ spl155_445
| ~ spl155_613 ),
inference(avatar_split_clause,[],[f18916,f18507,f9583,f19188]) ).
thf(f9583,plain,
( spl155_445
<=> ( $false = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),edges),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_445])]) ).
thf(f18507,plain,
( spl155_613
<=> ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X1),X0) )
| ( $false = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,X0),X1)),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_613])]) ).
thf(f18916,plain,
( ( $false = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) )
| ~ spl155_445
| ~ spl155_613 ),
inference(trivial_inequality_removal,[],[f18760]) ).
thf(f18760,plain,
( ( $true = $false )
| ( $false = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) )
| ~ spl155_445
| ~ spl155_613 ),
inference(superposition,[],[f18508,f9585]) ).
thf(f9585,plain,
( ( $false = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),edges),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) )
| ~ spl155_445 ),
inference(avatar_component_clause,[],[f9583]) ).
thf(f18508,plain,
( ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X1),X0) )
| ( $false = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,X0),X1)),X0) ) )
| ~ spl155_613 ),
inference(avatar_component_clause,[],[f18507]) ).
thf(f19186,plain,
( spl155_621
| ~ spl155_94
| ~ spl155_157 ),
inference(avatar_split_clause,[],[f4425,f4390,f3394,f19184]) ).
thf(f19184,plain,
( spl155_621
<=> ! [X0: set_Pr1986765409at_nat,X1: nat] :
( ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0) = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X1),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0)) )
| ( $true = vAPP(nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(nat,$o),sP1,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_621])]) ).
thf(f4425,plain,
( ! [X0: set_Pr1986765409at_nat,X1: nat] :
( ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0) = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X1),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0)) )
| ( $true = vAPP(nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(nat,$o),sP1,X0),X1) ) )
| ~ spl155_94
| ~ spl155_157 ),
inference(trivial_inequality_removal,[],[f4414]) ).
thf(f4414,plain,
( ! [X0: set_Pr1986765409at_nat,X1: nat] :
( ( $true != $true )
| ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0) = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X1),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0)) )
| ( $true = vAPP(nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(nat,$o),sP1,X0),X1) ) )
| ~ spl155_94
| ~ spl155_157 ),
inference(superposition,[],[f4391,f3395]) ).
thf(f18537,plain,
( spl155_620
| ~ spl155_76
| ~ spl155_158 ),
inference(avatar_split_clause,[],[f4455,f4394,f3244,f18535]) ).
thf(f18535,plain,
( spl155_620
<=> ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1) = X0 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_620])]) ).
thf(f4455,plain,
( ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1) = X0 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1)) ) )
| ~ spl155_76
| ~ spl155_158 ),
inference(trivial_inequality_removal,[],[f4430]) ).
thf(f4430,plain,
( ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true != $true )
| ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1) = X0 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1)) ) )
| ~ spl155_76
| ~ spl155_158 ),
inference(superposition,[],[f4395,f3245]) ).
thf(f18533,plain,
( spl155_619
| ~ spl155_77
| ~ spl155_158 ),
inference(avatar_split_clause,[],[f4454,f4394,f3248,f18531]) ).
thf(f18531,plain,
( spl155_619
<=> ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1) = X1 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X1),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_619])]) ).
thf(f4454,plain,
( ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1) = X1 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X1),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1)) ) )
| ~ spl155_77
| ~ spl155_158 ),
inference(trivial_inequality_removal,[],[f4431]) ).
thf(f4431,plain,
( ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true != $true )
| ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1) = X1 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X1),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1)) ) )
| ~ spl155_77
| ~ spl155_158 ),
inference(superposition,[],[f4395,f3249]) ).
thf(f18529,plain,
( spl155_618
| ~ spl155_75
| ~ spl155_157 ),
inference(avatar_split_clause,[],[f4428,f4390,f3240,f18527]) ).
thf(f18527,plain,
( spl155_618
<=> ! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X1) = X0 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_618])]) ).
thf(f4428,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X1) = X0 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X1)) ) )
| ~ spl155_75
| ~ spl155_157 ),
inference(trivial_inequality_removal,[],[f4411]) ).
thf(f4411,plain,
( ! [X0: nat,X1: nat] :
( ( $true != $true )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X1) = X0 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X1)) ) )
| ~ spl155_75
| ~ spl155_157 ),
inference(superposition,[],[f4391,f3241]) ).
thf(f18525,plain,
( spl155_617
| ~ spl155_74
| ~ spl155_157 ),
inference(avatar_split_clause,[],[f4427,f4390,f3236,f18523]) ).
thf(f18523,plain,
( spl155_617
<=> ! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X1) = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_617])]) ).
thf(f4427,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X1) = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X1)) ) )
| ~ spl155_74
| ~ spl155_157 ),
inference(trivial_inequality_removal,[],[f4412]) ).
thf(f4412,plain,
( ! [X0: nat,X1: nat] :
( ( $true != $true )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X1) = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X1)) ) )
| ~ spl155_74
| ~ spl155_157 ),
inference(superposition,[],[f4391,f3237]) ).
thf(f18521,plain,
( spl155_616
| ~ spl155_73
| ~ spl155_156 ),
inference(avatar_split_clause,[],[f4409,f4386,f3232,f18519]) ).
thf(f18519,plain,
( spl155_616
<=> ! [X0: set_nat,X1: set_nat] :
( ( vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X1) = X0 )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_616])]) ).
thf(f3232,plain,
( spl155_73
<=> ! [X0: set_nat,X1: set_nat] : ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X1)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_73])]) ).
thf(f4409,plain,
( ! [X0: set_nat,X1: set_nat] :
( ( vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X1) = X0 )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X1)) ) )
| ~ spl155_73
| ~ spl155_156 ),
inference(trivial_inequality_removal,[],[f4398]) ).
thf(f4398,plain,
( ! [X0: set_nat,X1: set_nat] :
( ( $true != $true )
| ( vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X1) = X0 )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X1)) ) )
| ~ spl155_73
| ~ spl155_156 ),
inference(superposition,[],[f4387,f3233]) ).
thf(f3233,plain,
( ! [X0: set_nat,X1: set_nat] : ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X1)),X0) )
| ~ spl155_73 ),
inference(avatar_component_clause,[],[f3232]) ).
thf(f18517,plain,
( spl155_615
| ~ spl155_72
| ~ spl155_156 ),
inference(avatar_split_clause,[],[f4408,f4386,f3228,f18515]) ).
thf(f18515,plain,
( spl155_615
<=> ! [X0: set_nat,X1: set_nat] :
( ( vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X1) = X1 )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X1),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_615])]) ).
thf(f3228,plain,
( spl155_72
<=> ! [X0: set_nat,X1: set_nat] : ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_72])]) ).
thf(f4408,plain,
( ! [X0: set_nat,X1: set_nat] :
( ( vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X1) = X1 )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X1),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X1)) ) )
| ~ spl155_72
| ~ spl155_156 ),
inference(trivial_inequality_removal,[],[f4399]) ).
thf(f4399,plain,
( ! [X0: set_nat,X1: set_nat] :
( ( $true != $true )
| ( vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X1) = X1 )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X1),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X1)) ) )
| ~ spl155_72
| ~ spl155_156 ),
inference(superposition,[],[f4387,f3229]) ).
thf(f3229,plain,
( ! [X0: set_nat,X1: set_nat] : ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X1)),X1) )
| ~ spl155_72 ),
inference(avatar_component_clause,[],[f3228]) ).
thf(f18513,plain,
( spl155_614
| ~ spl155_2
| ~ spl155_120 ),
inference(avatar_split_clause,[],[f3695,f3636,f2739,f18511]) ).
thf(f18511,plain,
( spl155_614
<=> ! [X0: set_Pr1986765409at_nat,X1: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK17,X0),X1)),X0) )
| ( $false = vAPP(nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(nat,$o),sP1,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_614])]) ).
thf(f3636,plain,
( spl155_120
<=> ! [X0: nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK17,X1),X0)),X1) )
| ( $true != vAPP(nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(nat,$o),sP1,X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_120])]) ).
thf(f3695,plain,
( ! [X0: set_Pr1986765409at_nat,X1: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK17,X0),X1)),X0) )
| ( $false = vAPP(nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(nat,$o),sP1,X0),X1) ) )
| ~ spl155_2
| ~ spl155_120 ),
inference(trivial_inequality_removal,[],[f3694]) ).
thf(f3694,plain,
( ! [X0: set_Pr1986765409at_nat,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK17,X0),X1)),X0) )
| ( $false = vAPP(nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(nat,$o),sP1,X0),X1) ) )
| ~ spl155_2
| ~ spl155_120 ),
inference(superposition,[],[f3637,f2740]) ).
thf(f3637,plain,
( ! [X0: nat,X1: set_Pr1986765409at_nat] :
( ( $true != vAPP(nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(nat,$o),sP1,X1),X0) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK17,X1),X0)),X1) ) )
| ~ spl155_120 ),
inference(avatar_component_clause,[],[f3636]) ).
thf(f18509,plain,
( spl155_613
| ~ spl155_2
| ~ spl155_118 ),
inference(avatar_split_clause,[],[f3661,f3628,f2739,f18507]) ).
thf(f3628,plain,
( spl155_118
<=> ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X1) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,X1),X0)),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_118])]) ).
thf(f3661,plain,
( ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X1),X0) )
| ( $false = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,X0),X1)),X0) ) )
| ~ spl155_2
| ~ spl155_118 ),
inference(trivial_inequality_removal,[],[f3660]) ).
thf(f3660,plain,
( ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X1),X0) )
| ( $false = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,X0),X1)),X0) ) )
| ~ spl155_2
| ~ spl155_118 ),
inference(superposition,[],[f3629,f2740]) ).
thf(f3629,plain,
( ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,X1),X0)),X1) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X1) ) )
| ~ spl155_118 ),
inference(avatar_component_clause,[],[f3628]) ).
thf(f18505,plain,
( spl155_612
| ~ spl155_2
| ~ spl155_116 ),
inference(avatar_split_clause,[],[f3642,f3620,f2739,f18503]) ).
thf(f18503,plain,
( spl155_612
<=> ! [X0: set_nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X1),X0) )
| ( $false = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,vAPP(set_nat,nat,vAPP(set_nat,sTfun(set_nat,nat),sK15,X0),X1)),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_612])]) ).
thf(f3620,plain,
( spl155_116
<=> ! [X0: set_nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),X1) )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,vAPP(set_nat,nat,vAPP(set_nat,sTfun(set_nat,nat),sK15,X1),X0)),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_116])]) ).
thf(f3642,plain,
( ! [X0: set_nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X1),X0) )
| ( $false = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,vAPP(set_nat,nat,vAPP(set_nat,sTfun(set_nat,nat),sK15,X0),X1)),X0) ) )
| ~ spl155_2
| ~ spl155_116 ),
inference(trivial_inequality_removal,[],[f3641]) ).
thf(f3641,plain,
( ! [X0: set_nat,X1: set_nat] :
( ( $true != $true )
| ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X1),X0) )
| ( $false = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,vAPP(set_nat,nat,vAPP(set_nat,sTfun(set_nat,nat),sK15,X0),X1)),X0) ) )
| ~ spl155_2
| ~ spl155_116 ),
inference(superposition,[],[f3621,f2740]) ).
thf(f3621,plain,
( ! [X0: set_nat,X1: set_nat] :
( ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,vAPP(set_nat,nat,vAPP(set_nat,sTfun(set_nat,nat),sK15,X1),X0)),X1) )
| ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),X1) ) )
| ~ spl155_116 ),
inference(avatar_component_clause,[],[f3620]) ).
thf(f18501,plain,
( spl155_611
| ~ spl155_125
| ~ spl155_460 ),
inference(avatar_split_clause,[],[f9954,f9835,f3763,f18499]) ).
thf(f18499,plain,
( spl155_611
<=> ! [X0: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,edges),X0)) )
| ( $false = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_611])]) ).
thf(f3763,plain,
( spl155_125
<=> ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),edges) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_125])]) ).
thf(f9835,plain,
( spl155_460
<=> ! [X2: set_Pr1986765409at_nat,X0: product_prod_nat_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X2),X1)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),X2) )
| ( $false = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_460])]) ).
thf(f9954,plain,
( ! [X0: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,edges),X0)) )
| ( $false = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),X0) ) )
| ~ spl155_125
| ~ spl155_460 ),
inference(trivial_inequality_removal,[],[f9928]) ).
thf(f9928,plain,
( ! [X0: set_Pr1986765409at_nat] :
( ( $true != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,edges),X0)) )
| ( $false = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),X0) ) )
| ~ spl155_125
| ~ spl155_460 ),
inference(superposition,[],[f9836,f3765]) ).
thf(f3765,plain,
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),edges) )
| ~ spl155_125 ),
inference(avatar_component_clause,[],[f3763]) ).
thf(f9836,plain,
( ! [X2: set_Pr1986765409at_nat,X0: product_prod_nat_nat,X1: set_Pr1986765409at_nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),X2) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X2),X1)) )
| ( $false = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),X1) ) )
| ~ spl155_460 ),
inference(avatar_component_clause,[],[f9835]) ).
thf(f18497,plain,
( spl155_610
| ~ spl155_2
| ~ spl155_115 ),
inference(avatar_split_clause,[],[f3640,f3616,f2739,f18495]) ).
thf(f18495,plain,
( spl155_610
<=> ! [X0: set_nat,X1: nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK14,X0),X1)),X0) )
| ( $false = vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_610])]) ).
thf(f3616,plain,
( spl155_115
<=> ! [X0: nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK14,X1),X0)),X1) )
| ( $true != vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_115])]) ).
thf(f3640,plain,
( ! [X0: set_nat,X1: nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK14,X0),X1)),X0) )
| ( $false = vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,X0),X1) ) )
| ~ spl155_2
| ~ spl155_115 ),
inference(trivial_inequality_removal,[],[f3639]) ).
thf(f3639,plain,
( ! [X0: set_nat,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK14,X0),X1)),X0) )
| ( $false = vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,X0),X1) ) )
| ~ spl155_2
| ~ spl155_115 ),
inference(superposition,[],[f3617,f2740]) ).
thf(f3617,plain,
( ! [X0: nat,X1: set_nat] :
( ( $true != vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,X1),X0) )
| ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK14,X1),X0)),X1) ) )
| ~ spl155_115 ),
inference(avatar_component_clause,[],[f3616]) ).
thf(f18361,plain,
( spl155_609
| ~ spl155_79
| ~ spl155_164 ),
inference(avatar_split_clause,[],[f4636,f4483,f3260,f18359]) ).
thf(f18359,plain,
( spl155_609
<=> ! [X0: set_Pr1986765409at_nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c))),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,c)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_609])]) ).
thf(f4636,plain,
( ! [X0: set_Pr1986765409at_nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c))),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,c)) )
| ~ spl155_79
| ~ spl155_164 ),
inference(trivial_inequality_removal,[],[f4621]) ).
thf(f4621,plain,
( ! [X0: set_Pr1986765409at_nat] :
( ( $true != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c))),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,c)) ) )
| ~ spl155_79
| ~ spl155_164 ),
inference(superposition,[],[f4484,f3262]) ).
thf(f18357,plain,
( spl155_608
| ~ spl155_79
| ~ spl155_163 ),
inference(avatar_split_clause,[],[f4608,f4479,f3260,f18355]) ).
thf(f18355,plain,
( spl155_608
<=> ! [X0: set_Pr1986765409at_nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),X0)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,c)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_608])]) ).
thf(f4608,plain,
( ! [X0: set_Pr1986765409at_nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),X0)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,c)) )
| ~ spl155_79
| ~ spl155_163 ),
inference(trivial_inequality_removal,[],[f4593]) ).
thf(f4593,plain,
( ! [X0: set_Pr1986765409at_nat] :
( ( $true != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),X0)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,c)) ) )
| ~ spl155_79
| ~ spl155_163 ),
inference(superposition,[],[f4480,f3262]) ).
thf(f16006,plain,
( spl155_607
| ~ spl155_15
| ~ spl155_478 ),
inference(avatar_split_clause,[],[f10702,f10491,f2860,f16004]) ).
thf(f16004,plain,
( spl155_607
<=> ! [X0: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,X0),edges)),edges) )
| ( $true = vAPP(product_prod_nat_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o),vAPP(sTfun(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o)),cCOMB,member701585322at_nat),X0),vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_607])]) ).
thf(f2860,plain,
( spl155_15
<=> ! [X0: set_Pr1986765409at_nat] : ( vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,vAPP(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o),vAPP(sTfun(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o)),cCOMB,member701585322at_nat),X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_15])]) ).
thf(f10491,plain,
( spl155_478
<=> ! [X0: product_prod_nat_nat > $o] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X0)),edges)),edges) )
| ( $true = vAPP(product_prod_nat_nat,$o,X0,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_478])]) ).
thf(f10702,plain,
( ! [X0: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,X0),edges)),edges) )
| ( $true = vAPP(product_prod_nat_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o),vAPP(sTfun(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o)),cCOMB,member701585322at_nat),X0),vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)) ) )
| ~ spl155_15
| ~ spl155_478 ),
inference(superposition,[],[f10492,f2861]) ).
thf(f2861,plain,
( ! [X0: set_Pr1986765409at_nat] : ( vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,vAPP(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o),vAPP(sTfun(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o)),cCOMB,member701585322at_nat),X0)) = X0 )
| ~ spl155_15 ),
inference(avatar_component_clause,[],[f2860]) ).
thf(f10492,plain,
( ! [X0: product_prod_nat_nat > $o] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X0)),edges)),edges) )
| ( $true = vAPP(product_prod_nat_nat,$o,X0,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)) ) )
| ~ spl155_478 ),
inference(avatar_component_clause,[],[f10491]) ).
thf(f15979,plain,
( spl155_606
| ~ spl155_246
| ~ spl155_314 ),
inference(avatar_split_clause,[],[f6985,f6949,f6132,f15977]) ).
thf(f15977,plain,
( spl155_606
<=> ! [X0: set_nat,X1: nat] :
( ( vAPP(list_nat,set_nat,set_nat2,vAPP(set_nat,list_nat,sK8,X0)) = X0 )
| ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_nat,set_nat,vAPP(nat,sTfun(set_nat,set_nat),sK10,X1),X0)),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_606])]) ).
thf(f6132,plain,
( spl155_246
<=> ! [X0: set_nat] :
( ( vAPP(list_nat,set_nat,set_nat2,vAPP(set_nat,list_nat,sK8,X0)) = X0 )
| ( $true != vAPP(set_nat,$o,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB))))),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_246])]) ).
thf(f6949,plain,
( spl155_314
<=> ! [X0: set_nat,X1: nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_nat,set_nat,vAPP(nat,sTfun(set_nat,set_nat),sK10,X1),X0)),X0) )
| ( $true = vAPP(set_nat,$o,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB))))),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_314])]) ).
thf(f6985,plain,
( ! [X0: set_nat,X1: nat] :
( ( vAPP(list_nat,set_nat,set_nat2,vAPP(set_nat,list_nat,sK8,X0)) = X0 )
| ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_nat,set_nat,vAPP(nat,sTfun(set_nat,set_nat),sK10,X1),X0)),X0) ) )
| ~ spl155_246
| ~ spl155_314 ),
inference(trivial_inequality_removal,[],[f6984]) ).
thf(f6984,plain,
( ! [X0: set_nat,X1: nat] :
( ( $true != $true )
| ( vAPP(list_nat,set_nat,set_nat2,vAPP(set_nat,list_nat,sK8,X0)) = X0 )
| ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_nat,set_nat,vAPP(nat,sTfun(set_nat,set_nat),sK10,X1),X0)),X0) ) )
| ~ spl155_246
| ~ spl155_314 ),
inference(superposition,[],[f6133,f6950]) ).
thf(f6950,plain,
( ! [X0: set_nat,X1: nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_nat,set_nat,vAPP(nat,sTfun(set_nat,set_nat),sK10,X1),X0)),X0) )
| ( $true = vAPP(set_nat,$o,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB))))),X0) ) )
| ~ spl155_314 ),
inference(avatar_component_clause,[],[f6949]) ).
thf(f6133,plain,
( ! [X0: set_nat] :
( ( $true != vAPP(set_nat,$o,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB))))),X0) )
| ( vAPP(list_nat,set_nat,set_nat2,vAPP(set_nat,list_nat,sK8,X0)) = X0 ) )
| ~ spl155_246 ),
inference(avatar_component_clause,[],[f6132]) ).
thf(f15975,plain,
( spl155_605
| ~ spl155_105
| ~ spl155_155 ),
inference(avatar_split_clause,[],[f4379,f4326,f3488,f15973]) ).
thf(f15973,plain,
( spl155_605
<=> ! [X0: nat,X1: set_Pr1986765409at_nat] :
( ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK28,X1),X0)) = X0 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_605])]) ).
thf(f3488,plain,
( spl155_105
<=> ! [X0: nat,X1: set_Pr1986765409at_nat] :
( ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK28,X1),X0)) = X0 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_105])]) ).
thf(f4379,plain,
( ! [X0: nat,X1: set_Pr1986765409at_nat] :
( ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK28,X1),X0)) = X0 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)),X0) ) )
| ~ spl155_105
| ~ spl155_155 ),
inference(trivial_inequality_removal,[],[f4337]) ).
thf(f4337,plain,
( ! [X0: nat,X1: set_Pr1986765409at_nat] :
( ( $true != $true )
| ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK28,X1),X0)) = X0 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)),X0) ) )
| ~ spl155_105
| ~ spl155_155 ),
inference(superposition,[],[f3489,f4327]) ).
thf(f3489,plain,
( ! [X0: nat,X1: set_Pr1986765409at_nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)) )
| ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK28,X1),X0)) = X0 ) )
| ~ spl155_105 ),
inference(avatar_component_clause,[],[f3488]) ).
thf(f15971,plain,
( spl155_604
| ~ spl155_104
| ~ spl155_155 ),
inference(avatar_split_clause,[],[f4378,f4326,f3484,f15969]) ).
thf(f15969,plain,
( spl155_604
<=> ! [X0: nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK28,X1),X0)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_604])]) ).
thf(f3484,plain,
( spl155_104
<=> ! [X0: nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK28,X1),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_104])]) ).
thf(f4378,plain,
( ! [X0: nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK28,X1),X0)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)),X0) ) )
| ~ spl155_104
| ~ spl155_155 ),
inference(trivial_inequality_removal,[],[f4338]) ).
thf(f4338,plain,
( ! [X0: nat,X1: set_Pr1986765409at_nat] :
( ( $true != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK28,X1),X0)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)),X0) ) )
| ~ spl155_104
| ~ spl155_155 ),
inference(superposition,[],[f3485,f4327]) ).
thf(f3485,plain,
( ! [X0: nat,X1: set_Pr1986765409at_nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK28,X1),X0)) ) )
| ~ spl155_104 ),
inference(avatar_component_clause,[],[f3484]) ).
thf(f15967,plain,
( spl155_603
| ~ spl155_103
| ~ spl155_155 ),
inference(avatar_split_clause,[],[f4377,f4326,f3480,f15965]) ).
thf(f15965,plain,
( spl155_603
<=> ! [X0: nat,X1: set_nat] :
( ( vAPP(set_nat,nat,finite_card_nat,vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK27,X1),X0)) = X0 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_nat,nat,finite_card_nat,X1)),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_603])]) ).
thf(f3480,plain,
( spl155_103
<=> ! [X0: nat,X1: set_nat] :
( ( vAPP(set_nat,nat,finite_card_nat,vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK27,X1),X0)) = X0 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),vAPP(set_nat,nat,finite_card_nat,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_103])]) ).
thf(f4377,plain,
( ! [X0: nat,X1: set_nat] :
( ( vAPP(set_nat,nat,finite_card_nat,vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK27,X1),X0)) = X0 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_nat,nat,finite_card_nat,X1)),X0) ) )
| ~ spl155_103
| ~ spl155_155 ),
inference(trivial_inequality_removal,[],[f4339]) ).
thf(f4339,plain,
( ! [X0: nat,X1: set_nat] :
( ( $true != $true )
| ( vAPP(set_nat,nat,finite_card_nat,vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK27,X1),X0)) = X0 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_nat,nat,finite_card_nat,X1)),X0) ) )
| ~ spl155_103
| ~ spl155_155 ),
inference(superposition,[],[f3481,f4327]) ).
thf(f3481,plain,
( ! [X0: nat,X1: set_nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),vAPP(set_nat,nat,finite_card_nat,X1)) )
| ( vAPP(set_nat,nat,finite_card_nat,vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK27,X1),X0)) = X0 ) )
| ~ spl155_103 ),
inference(avatar_component_clause,[],[f3480]) ).
thf(f15963,plain,
( spl155_602
| ~ spl155_2
| ~ spl155_114 ),
inference(avatar_split_clause,[],[f3610,f3524,f2739,f15961]) ).
thf(f15961,plain,
( spl155_602
<=> ! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),X1) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP2,X0),X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_602])]) ).
thf(f3524,plain,
( spl155_114
<=> ! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X2),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP2,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_114])]) ).
thf(f3610,plain,
( ! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),X1) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP2,X0),X1),X2) ) )
| ~ spl155_2
| ~ spl155_114 ),
inference(trivial_inequality_removal,[],[f3609]) ).
thf(f3609,plain,
( ! [X2: nat,X0: nat,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),X1) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP2,X0),X1),X2) ) )
| ~ spl155_2
| ~ spl155_114 ),
inference(superposition,[],[f3525,f2740]) ).
thf(f3525,plain,
( ! [X2: nat,X0: nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP2,X2),X1),X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X2),X1) ) )
| ~ spl155_114 ),
inference(avatar_component_clause,[],[f3524]) ).
thf(f15959,plain,
( spl155_601
| ~ spl155_2
| ~ spl155_113 ),
inference(avatar_split_clause,[],[f3608,f3520,f2739,f15957]) ).
thf(f15957,plain,
( spl155_601
<=> ! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X1),X2) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP2,X0),X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_601])]) ).
thf(f3520,plain,
( spl155_113
<=> ! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X1),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP2,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_113])]) ).
thf(f3608,plain,
( ! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X1),X2) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP2,X0),X1),X2) ) )
| ~ spl155_2
| ~ spl155_113 ),
inference(trivial_inequality_removal,[],[f3607]) ).
thf(f3607,plain,
( ! [X2: nat,X0: nat,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X1),X2) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP2,X0),X1),X2) ) )
| ~ spl155_2
| ~ spl155_113 ),
inference(superposition,[],[f3521,f2740]) ).
thf(f3521,plain,
( ! [X2: nat,X0: nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP2,X2),X1),X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X1),X0) ) )
| ~ spl155_113 ),
inference(avatar_component_clause,[],[f3520]) ).
thf(f15955,plain,
( spl155_600
| ~ spl155_2
| ~ spl155_112 ),
inference(avatar_split_clause,[],[f3606,f3516,f2739,f15953]) ).
thf(f15953,plain,
( spl155_600
<=> ! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),X1) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP3,X0),X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_600])]) ).
thf(f3516,plain,
( spl155_112
<=> ! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X2),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP3,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_112])]) ).
thf(f3606,plain,
( ! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),X1) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP3,X0),X1),X2) ) )
| ~ spl155_2
| ~ spl155_112 ),
inference(trivial_inequality_removal,[],[f3605]) ).
thf(f3605,plain,
( ! [X2: nat,X0: nat,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),X1) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP3,X0),X1),X2) ) )
| ~ spl155_2
| ~ spl155_112 ),
inference(superposition,[],[f3517,f2740]) ).
thf(f3517,plain,
( ! [X2: nat,X0: nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP3,X2),X1),X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X2),X1) ) )
| ~ spl155_112 ),
inference(avatar_component_clause,[],[f3516]) ).
thf(f15951,plain,
( spl155_599
| ~ spl155_2
| ~ spl155_111 ),
inference(avatar_split_clause,[],[f3604,f3512,f2739,f15949]) ).
thf(f15949,plain,
( spl155_599
<=> ! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X1),X2) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP3,X0),X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_599])]) ).
thf(f3512,plain,
( spl155_111
<=> ! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X1),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP3,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_111])]) ).
thf(f3604,plain,
( ! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X1),X2) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP3,X0),X1),X2) ) )
| ~ spl155_2
| ~ spl155_111 ),
inference(trivial_inequality_removal,[],[f3603]) ).
thf(f3603,plain,
( ! [X2: nat,X0: nat,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X1),X2) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP3,X0),X1),X2) ) )
| ~ spl155_2
| ~ spl155_111 ),
inference(superposition,[],[f3513,f2740]) ).
thf(f3513,plain,
( ! [X2: nat,X0: nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP3,X2),X1),X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X1),X0) ) )
| ~ spl155_111 ),
inference(avatar_component_clause,[],[f3512]) ).
thf(f15947,plain,
( spl155_598
| ~ spl155_2
| ~ spl155_110 ),
inference(avatar_split_clause,[],[f3602,f3508,f2739,f15945]) ).
thf(f15945,plain,
( spl155_598
<=> ! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),X1) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP4,X0),X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_598])]) ).
thf(f3508,plain,
( spl155_110
<=> ! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X2),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP4,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_110])]) ).
thf(f3602,plain,
( ! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),X1) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP4,X0),X1),X2) ) )
| ~ spl155_2
| ~ spl155_110 ),
inference(trivial_inequality_removal,[],[f3601]) ).
thf(f3601,plain,
( ! [X2: nat,X0: nat,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),X1) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP4,X0),X1),X2) ) )
| ~ spl155_2
| ~ spl155_110 ),
inference(superposition,[],[f3509,f2740]) ).
thf(f3509,plain,
( ! [X2: nat,X0: nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP4,X2),X1),X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X2),X1) ) )
| ~ spl155_110 ),
inference(avatar_component_clause,[],[f3508]) ).
thf(f15922,plain,
( spl155_597
| ~ spl155_2
| ~ spl155_109 ),
inference(avatar_split_clause,[],[f3600,f3504,f2739,f15920]) ).
thf(f15920,plain,
( spl155_597
<=> ! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X1),X2) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP4,X0),X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_597])]) ).
thf(f3504,plain,
( spl155_109
<=> ! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X1),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP4,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_109])]) ).
thf(f3600,plain,
( ! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X1),X2) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP4,X0),X1),X2) ) )
| ~ spl155_2
| ~ spl155_109 ),
inference(trivial_inequality_removal,[],[f3599]) ).
thf(f3599,plain,
( ! [X2: nat,X0: nat,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X1),X2) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP4,X0),X1),X2) ) )
| ~ spl155_2
| ~ spl155_109 ),
inference(superposition,[],[f3505,f2740]) ).
thf(f3505,plain,
( ! [X2: nat,X0: nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP4,X2),X1),X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X1),X0) ) )
| ~ spl155_109 ),
inference(avatar_component_clause,[],[f3504]) ).
thf(f15918,plain,
( spl155_596
| ~ spl155_2
| ~ spl155_108 ),
inference(avatar_split_clause,[],[f3598,f3500,f2739,f15916]) ).
thf(f15916,plain,
( spl155_596
<=> ! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),X1) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP5,X0),X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_596])]) ).
thf(f3500,plain,
( spl155_108
<=> ! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X2),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP5,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_108])]) ).
thf(f3598,plain,
( ! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),X1) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP5,X0),X1),X2) ) )
| ~ spl155_2
| ~ spl155_108 ),
inference(trivial_inequality_removal,[],[f3597]) ).
thf(f3597,plain,
( ! [X2: nat,X0: nat,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),X1) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP5,X0),X1),X2) ) )
| ~ spl155_2
| ~ spl155_108 ),
inference(superposition,[],[f3501,f2740]) ).
thf(f3501,plain,
( ! [X2: nat,X0: nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP5,X2),X1),X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X2),X1) ) )
| ~ spl155_108 ),
inference(avatar_component_clause,[],[f3500]) ).
thf(f15914,plain,
( spl155_595
| ~ spl155_2
| ~ spl155_107 ),
inference(avatar_split_clause,[],[f3596,f3496,f2739,f15912]) ).
thf(f15912,plain,
( spl155_595
<=> ! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X1),X2) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP5,X0),X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_595])]) ).
thf(f3496,plain,
( spl155_107
<=> ! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X1),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP5,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_107])]) ).
thf(f3596,plain,
( ! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X1),X2) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP5,X0),X1),X2) ) )
| ~ spl155_2
| ~ spl155_107 ),
inference(trivial_inequality_removal,[],[f3595]) ).
thf(f3595,plain,
( ! [X2: nat,X0: nat,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X1),X2) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP5,X0),X1),X2) ) )
| ~ spl155_2
| ~ spl155_107 ),
inference(superposition,[],[f3497,f2740]) ).
thf(f3497,plain,
( ! [X2: nat,X0: nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP5,X2),X1),X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X1),X0) ) )
| ~ spl155_107 ),
inference(avatar_component_clause,[],[f3496]) ).
thf(f15910,plain,
( spl155_594
| ~ spl155_2
| ~ spl155_105 ),
inference(avatar_split_clause,[],[f3589,f3488,f2739,f15908]) ).
thf(f15908,plain,
( spl155_594
<=> ! [X0: nat,X1: set_Pr1986765409at_nat] :
( ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK28,X1),X0)) = X0 )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_594])]) ).
thf(f3589,plain,
( ! [X0: nat,X1: set_Pr1986765409at_nat] :
( ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK28,X1),X0)) = X0 )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)) ) )
| ~ spl155_2
| ~ spl155_105 ),
inference(trivial_inequality_removal,[],[f3588]) ).
thf(f3588,plain,
( ! [X0: nat,X1: set_Pr1986765409at_nat] :
( ( $true != $true )
| ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK28,X1),X0)) = X0 )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)) ) )
| ~ spl155_2
| ~ spl155_105 ),
inference(superposition,[],[f3489,f2740]) ).
thf(f15906,plain,
( spl155_593
| ~ spl155_2
| ~ spl155_104 ),
inference(avatar_split_clause,[],[f3576,f3484,f2739,f15904]) ).
thf(f15904,plain,
( spl155_593
<=> ! [X0: nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK28,X1),X0)) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_593])]) ).
thf(f3576,plain,
( ! [X0: nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK28,X1),X0)) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)) ) )
| ~ spl155_2
| ~ spl155_104 ),
inference(trivial_inequality_removal,[],[f3575]) ).
thf(f3575,plain,
( ! [X0: nat,X1: set_Pr1986765409at_nat] :
( ( $true != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK28,X1),X0)) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)) ) )
| ~ spl155_2
| ~ spl155_104 ),
inference(superposition,[],[f3485,f2740]) ).
thf(f15902,plain,
( spl155_592
| ~ spl155_2
| ~ spl155_103 ),
inference(avatar_split_clause,[],[f3557,f3480,f2739,f15900]) ).
thf(f15900,plain,
( spl155_592
<=> ! [X0: nat,X1: set_nat] :
( ( vAPP(set_nat,nat,finite_card_nat,vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK27,X1),X0)) = X0 )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),vAPP(set_nat,nat,finite_card_nat,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_592])]) ).
thf(f3557,plain,
( ! [X0: nat,X1: set_nat] :
( ( vAPP(set_nat,nat,finite_card_nat,vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK27,X1),X0)) = X0 )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),vAPP(set_nat,nat,finite_card_nat,X1)) ) )
| ~ spl155_2
| ~ spl155_103 ),
inference(trivial_inequality_removal,[],[f3556]) ).
thf(f3556,plain,
( ! [X0: nat,X1: set_nat] :
( ( $true != $true )
| ( vAPP(set_nat,nat,finite_card_nat,vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK27,X1),X0)) = X0 )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),vAPP(set_nat,nat,finite_card_nat,X1)) ) )
| ~ spl155_2
| ~ spl155_103 ),
inference(superposition,[],[f3481,f2740]) ).
thf(f15898,plain,
( spl155_591
| ~ spl155_2
| ~ spl155_102 ),
inference(avatar_split_clause,[],[f3538,f3476,f2739,f15896]) ).
thf(f15896,plain,
( spl155_591
<=> ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0) != vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1) )
| ( X0 = X1 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X1) )
| ( $false = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_591])]) ).
thf(f3476,plain,
( spl155_102
<=> ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( X0 = X1 )
| ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0) != vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X1),X0) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_102])]) ).
thf(f3538,plain,
( ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0) != vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1) )
| ( X0 = X1 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X1) )
| ( $false = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X1) ) )
| ~ spl155_2
| ~ spl155_102 ),
inference(trivial_inequality_removal,[],[f3537]) ).
thf(f3537,plain,
( ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true != $true )
| ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0) != vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1) )
| ( X0 = X1 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X1) )
| ( $false = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X1) ) )
| ~ spl155_2
| ~ spl155_102 ),
inference(superposition,[],[f3477,f2740]) ).
thf(f3477,plain,
( ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X1),X0) )
| ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0) != vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1) )
| ( X0 = X1 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) ) )
| ~ spl155_102 ),
inference(avatar_component_clause,[],[f3476]) ).
thf(f15652,plain,
( spl155_590
| ~ spl155_181
| ~ spl155_573 ),
inference(avatar_split_clause,[],[f14752,f14470,f4909,f15650]) ).
thf(f15650,plain,
( spl155_590
<=> ! [X0: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),edges)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,X0),edges)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_590])]) ).
thf(f4909,plain,
( spl155_181
<=> ! [X0: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),edges)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_181])]) ).
thf(f14470,plain,
( spl155_573
<=> ! [X0: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,X0),edges)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_573])]) ).
thf(f14752,plain,
( ! [X0: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),edges)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,X0),edges)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p)) ) )
| ~ spl155_181
| ~ spl155_573 ),
inference(trivial_inequality_removal,[],[f14713]) ).
thf(f14713,plain,
( ! [X0: set_Pr1986765409at_nat] :
( ( $true != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),edges)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,X0),edges)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p)) ) )
| ~ spl155_181
| ~ spl155_573 ),
inference(superposition,[],[f4910,f14471]) ).
thf(f14471,plain,
( ! [X0: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),X0) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,X0),edges)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p)) ) )
| ~ spl155_573 ),
inference(avatar_component_clause,[],[f14470]) ).
thf(f4910,plain,
( ! [X0: set_Pr1986765409at_nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),X0) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),edges)) ) )
| ~ spl155_181 ),
inference(avatar_component_clause,[],[f4909]) ).
thf(f14795,plain,
( spl155_589
| ~ spl155_4
| ~ spl155_79
| ~ spl155_174 ),
inference(avatar_split_clause,[],[f4819,f4786,f3260,f2775,f14792]) ).
thf(f14792,plain,
( spl155_589
<=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c))),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,c))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_589])]) ).
thf(f2775,plain,
( spl155_4
<=> ( vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,c)) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_4])]) ).
thf(f4819,plain,
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c))),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,c))) )
| ~ spl155_4
| ~ spl155_79
| ~ spl155_174 ),
inference(trivial_inequality_removal,[],[f4818]) ).
thf(f4818,plain,
( ( $true != $true )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c))),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,c))) )
| ~ spl155_4
| ~ spl155_79
| ~ spl155_174 ),
inference(forward_demodulation,[],[f4810,f2777]) ).
thf(f2777,plain,
( ( vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,c)) = $true )
| ~ spl155_4 ),
inference(avatar_component_clause,[],[f2775]) ).
thf(f4810,plain,
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c))),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,c))) )
| ( vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,c)) != $true )
| ~ spl155_79
| ~ spl155_174 ),
inference(trivial_inequality_removal,[],[f4795]) ).
thf(f4795,plain,
( ( $true != $true )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c))),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,c))) )
| ( vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,c)) != $true )
| ~ spl155_79
| ~ spl155_174 ),
inference(superposition,[],[f4787,f3262]) ).
thf(f14790,plain,
( spl155_588
| ~ spl155_76
| ~ spl155_164 ),
inference(avatar_split_clause,[],[f4641,f4483,f3244,f14788]) ).
thf(f14788,plain,
( spl155_588
<=> ! [X2: set_Pr1986765409at_nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X2),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_588])]) ).
thf(f4641,plain,
( ! [X2: set_Pr1986765409at_nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X2),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1))),X0) )
| ~ spl155_76
| ~ spl155_164 ),
inference(trivial_inequality_removal,[],[f4616]) ).
thf(f4616,plain,
( ! [X2: set_Pr1986765409at_nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X2),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1))),X0) ) )
| ~ spl155_76
| ~ spl155_164 ),
inference(superposition,[],[f4484,f3245]) ).
thf(f14786,plain,
( spl155_587
| ~ spl155_77
| ~ spl155_164 ),
inference(avatar_split_clause,[],[f4640,f4483,f3248,f14784]) ).
thf(f14784,plain,
( spl155_587
<=> ! [X2: set_Pr1986765409at_nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X2),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_587])]) ).
thf(f4640,plain,
( ! [X2: set_Pr1986765409at_nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X2),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1))),X1) )
| ~ spl155_77
| ~ spl155_164 ),
inference(trivial_inequality_removal,[],[f4617]) ).
thf(f4617,plain,
( ! [X2: set_Pr1986765409at_nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X2),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1))),X1) ) )
| ~ spl155_77
| ~ spl155_164 ),
inference(superposition,[],[f4484,f3249]) ).
thf(f14782,plain,
( spl155_586
| ~ spl155_76
| ~ spl155_163 ),
inference(avatar_split_clause,[],[f4613,f4479,f3244,f14780]) ).
thf(f14780,plain,
( spl155_586
<=> ! [X2: set_Pr1986765409at_nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1)),X2)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_586])]) ).
thf(f4613,plain,
( ! [X2: set_Pr1986765409at_nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1)),X2)),X0) )
| ~ spl155_76
| ~ spl155_163 ),
inference(trivial_inequality_removal,[],[f4588]) ).
thf(f4588,plain,
( ! [X2: set_Pr1986765409at_nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1)),X2)),X0) ) )
| ~ spl155_76
| ~ spl155_163 ),
inference(superposition,[],[f4480,f3245]) ).
thf(f14778,plain,
( spl155_585
| ~ spl155_77
| ~ spl155_163 ),
inference(avatar_split_clause,[],[f4612,f4479,f3248,f14776]) ).
thf(f14776,plain,
( spl155_585
<=> ! [X2: set_Pr1986765409at_nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1)),X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_585])]) ).
thf(f4612,plain,
( ! [X2: set_Pr1986765409at_nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1)),X2)),X1) )
| ~ spl155_77
| ~ spl155_163 ),
inference(trivial_inequality_removal,[],[f4589]) ).
thf(f4589,plain,
( ! [X2: set_Pr1986765409at_nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1)),X2)),X1) ) )
| ~ spl155_77
| ~ spl155_163 ),
inference(superposition,[],[f4480,f3249]) ).
thf(f14774,plain,
( spl155_584
| ~ spl155_75
| ~ spl155_162 ),
inference(avatar_split_clause,[],[f4585,f4475,f3240,f14772]) ).
thf(f14772,plain,
( spl155_584
<=> ! [X2: nat,X0: nat,X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X1)),X2)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_584])]) ).
thf(f4585,plain,
( ! [X2: nat,X0: nat,X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X1)),X2)),X0) )
| ~ spl155_75
| ~ spl155_162 ),
inference(trivial_inequality_removal,[],[f4566]) ).
thf(f4566,plain,
( ! [X2: nat,X0: nat,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X1)),X2)),X0) ) )
| ~ spl155_75
| ~ spl155_162 ),
inference(superposition,[],[f4476,f3241]) ).
thf(f14770,plain,
( spl155_583
| ~ spl155_74
| ~ spl155_162 ),
inference(avatar_split_clause,[],[f4584,f4475,f3236,f14768]) ).
thf(f14768,plain,
( spl155_583
<=> ! [X2: nat,X0: nat,X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X1)),X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_583])]) ).
thf(f4584,plain,
( ! [X2: nat,X0: nat,X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X1)),X2)),X1) )
| ~ spl155_74
| ~ spl155_162 ),
inference(trivial_inequality_removal,[],[f4567]) ).
thf(f4567,plain,
( ! [X2: nat,X0: nat,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X1)),X2)),X1) ) )
| ~ spl155_74
| ~ spl155_162 ),
inference(superposition,[],[f4476,f3237]) ).
thf(f14766,plain,
( spl155_582
| ~ spl155_75
| ~ spl155_161 ),
inference(avatar_split_clause,[],[f4563,f4471,f3240,f14764]) ).
thf(f14764,plain,
( spl155_582
<=> ! [X2: nat,X0: nat,X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X1))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_582])]) ).
thf(f4563,plain,
( ! [X2: nat,X0: nat,X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X1))),X0) )
| ~ spl155_75
| ~ spl155_161 ),
inference(trivial_inequality_removal,[],[f4544]) ).
thf(f4544,plain,
( ! [X2: nat,X0: nat,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X1))),X0) ) )
| ~ spl155_75
| ~ spl155_161 ),
inference(superposition,[],[f4472,f3241]) ).
thf(f14762,plain,
( spl155_581
| ~ spl155_74
| ~ spl155_161 ),
inference(avatar_split_clause,[],[f4562,f4471,f3236,f14760]) ).
thf(f14760,plain,
( spl155_581
<=> ! [X2: nat,X0: nat,X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X1))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_581])]) ).
thf(f4562,plain,
( ! [X2: nat,X0: nat,X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X1))),X1) )
| ~ spl155_74
| ~ spl155_161 ),
inference(trivial_inequality_removal,[],[f4545]) ).
thf(f4545,plain,
( ! [X2: nat,X0: nat,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X1))),X1) ) )
| ~ spl155_74
| ~ spl155_161 ),
inference(superposition,[],[f4472,f3237]) ).
thf(f14758,plain,
( spl155_580
| ~ spl155_73
| ~ spl155_160 ),
inference(avatar_split_clause,[],[f4541,f4467,f3232,f14756]) ).
thf(f14756,plain,
( spl155_580
<=> ! [X2: set_nat,X0: set_nat,X1: set_nat] : ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X1)),X2)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_580])]) ).
thf(f4467,plain,
( spl155_160
<=> ! [X2: set_nat,X0: set_nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X2)),X1) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_160])]) ).
thf(f4541,plain,
( ! [X2: set_nat,X0: set_nat,X1: set_nat] : ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X1)),X2)),X0) )
| ~ spl155_73
| ~ spl155_160 ),
inference(trivial_inequality_removal,[],[f4530]) ).
thf(f4530,plain,
( ! [X2: set_nat,X0: set_nat,X1: set_nat] :
( ( $true != $true )
| ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X1)),X2)),X0) ) )
| ~ spl155_73
| ~ spl155_160 ),
inference(superposition,[],[f4468,f3233]) ).
thf(f4468,plain,
( ! [X2: set_nat,X0: set_nat,X1: set_nat] :
( ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),X1) )
| ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X2)),X1) ) )
| ~ spl155_160 ),
inference(avatar_component_clause,[],[f4467]) ).
thf(f14710,plain,
( spl155_579
| ~ spl155_72
| ~ spl155_160 ),
inference(avatar_split_clause,[],[f4540,f4467,f3228,f14708]) ).
thf(f14708,plain,
( spl155_579
<=> ! [X2: set_nat,X0: set_nat,X1: set_nat] : ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X1)),X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_579])]) ).
thf(f4540,plain,
( ! [X2: set_nat,X0: set_nat,X1: set_nat] : ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X1)),X2)),X1) )
| ~ spl155_72
| ~ spl155_160 ),
inference(trivial_inequality_removal,[],[f4531]) ).
thf(f4531,plain,
( ! [X2: set_nat,X0: set_nat,X1: set_nat] :
( ( $true != $true )
| ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X1)),X2)),X1) ) )
| ~ spl155_72
| ~ spl155_160 ),
inference(superposition,[],[f4468,f3229]) ).
thf(f14706,plain,
( spl155_578
| ~ spl155_73
| ~ spl155_159 ),
inference(avatar_split_clause,[],[f4527,f4463,f3232,f14704]) ).
thf(f14704,plain,
( spl155_578
<=> ! [X2: set_nat,X0: set_nat,X1: set_nat] : ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X2),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X1))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_578])]) ).
thf(f4463,plain,
( spl155_159
<=> ! [X2: set_nat,X0: set_nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X2),X0)),X1) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_159])]) ).
thf(f4527,plain,
( ! [X2: set_nat,X0: set_nat,X1: set_nat] : ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X2),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X1))),X0) )
| ~ spl155_73
| ~ spl155_159 ),
inference(trivial_inequality_removal,[],[f4516]) ).
thf(f4516,plain,
( ! [X2: set_nat,X0: set_nat,X1: set_nat] :
( ( $true != $true )
| ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X2),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X1))),X0) ) )
| ~ spl155_73
| ~ spl155_159 ),
inference(superposition,[],[f4464,f3233]) ).
thf(f4464,plain,
( ! [X2: set_nat,X0: set_nat,X1: set_nat] :
( ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),X1) )
| ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X2),X0)),X1) ) )
| ~ spl155_159 ),
inference(avatar_component_clause,[],[f4463]) ).
thf(f14702,plain,
( spl155_577
| ~ spl155_72
| ~ spl155_159 ),
inference(avatar_split_clause,[],[f4526,f4463,f3228,f14700]) ).
thf(f14700,plain,
( spl155_577
<=> ! [X2: set_nat,X0: set_nat,X1: set_nat] : ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X2),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X1))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_577])]) ).
thf(f4526,plain,
( ! [X2: set_nat,X0: set_nat,X1: set_nat] : ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X2),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X1))),X1) )
| ~ spl155_72
| ~ spl155_159 ),
inference(trivial_inequality_removal,[],[f4517]) ).
thf(f4517,plain,
( ! [X2: set_nat,X0: set_nat,X1: set_nat] :
( ( $true != $true )
| ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X2),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X1))),X1) ) )
| ~ spl155_72
| ~ spl155_159 ),
inference(superposition,[],[f4464,f3229]) ).
thf(f14546,plain,
( spl155_576
| ~ spl155_100
| ~ spl155_155 ),
inference(avatar_split_clause,[],[f4376,f4326,f3436,f14544]) ).
thf(f14544,plain,
( spl155_576
<=> ! [X0: product_prod_nat_nat,X1: list_P559422087at_nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(list_P559422087at_nat,nat,size_s1990949619at_nat,X1)),vAPP(list_P559422087at_nat,nat,size_s1990949619at_nat,vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_576])]) ).
thf(f3436,plain,
( spl155_100
<=> ! [X2: product_prod_nat_nat,X1: list_P559422087at_nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(list_P559422087at_nat,nat,size_s1990949619at_nat,vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,X2),X1))),vAPP(list_P559422087at_nat,nat,size_s1990949619at_nat,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_100])]) ).
thf(f4376,plain,
( ! [X0: product_prod_nat_nat,X1: list_P559422087at_nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(list_P559422087at_nat,nat,size_s1990949619at_nat,X1)),vAPP(list_P559422087at_nat,nat,size_s1990949619at_nat,vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,X0),X1))) )
| ~ spl155_100
| ~ spl155_155 ),
inference(trivial_inequality_removal,[],[f4340]) ).
thf(f4340,plain,
( ! [X0: product_prod_nat_nat,X1: list_P559422087at_nat] :
( ( $true != $true )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(list_P559422087at_nat,nat,size_s1990949619at_nat,X1)),vAPP(list_P559422087at_nat,nat,size_s1990949619at_nat,vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,X0),X1))) ) )
| ~ spl155_100
| ~ spl155_155 ),
inference(superposition,[],[f3437,f4327]) ).
thf(f3437,plain,
( ! [X2: product_prod_nat_nat,X1: list_P559422087at_nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(list_P559422087at_nat,nat,size_s1990949619at_nat,vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,X2),X1))),vAPP(list_P559422087at_nat,nat,size_s1990949619at_nat,X1)) )
| ~ spl155_100 ),
inference(avatar_component_clause,[],[f3436]) ).
thf(f14542,plain,
( spl155_575
| ~ spl155_8
| ~ spl155_139 ),
inference(avatar_split_clause,[],[f3976,f3968,f2801,f14539]) ).
thf(f14539,plain,
( spl155_575
<=> ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),reachableNodes_a,c),s)),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,c)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_575])]) ).
thf(f2801,plain,
( spl155_8
<=> ( vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,s),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,c)) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_8])]) ).
thf(f3968,plain,
( spl155_139
<=> ! [X0: nat,X1: product_prod_nat_nat > a] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),reachableNodes_a,X1),X0)),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X1)) )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_139])]) ).
thf(f3976,plain,
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),reachableNodes_a,c),s)),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,c)) )
| ~ spl155_8
| ~ spl155_139 ),
inference(trivial_inequality_removal,[],[f3971]) ).
thf(f3971,plain,
( ( $true != $true )
| ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),reachableNodes_a,c),s)),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,c)) )
| ~ spl155_8
| ~ spl155_139 ),
inference(superposition,[],[f3969,f2803]) ).
thf(f2803,plain,
( ( vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,s),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,c)) = $true )
| ~ spl155_8 ),
inference(avatar_component_clause,[],[f2801]) ).
thf(f3969,plain,
( ! [X0: nat,X1: product_prod_nat_nat > a] :
( ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X1)) )
| ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),reachableNodes_a,X1),X0)),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X1)) ) )
| ~ spl155_139 ),
inference(avatar_component_clause,[],[f3968]) ).
thf(f14537,plain,
( spl155_574
| ~ spl155_2
| ~ spl155_100 ),
inference(avatar_split_clause,[],[f3474,f3436,f2739,f14535]) ).
thf(f14535,plain,
( spl155_574
<=> ! [X0: product_prod_nat_nat,X1: list_P559422087at_nat] : ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(list_P559422087at_nat,nat,size_s1990949619at_nat,vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,X0),X1))),vAPP(list_P559422087at_nat,nat,size_s1990949619at_nat,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_574])]) ).
thf(f3474,plain,
( ! [X0: product_prod_nat_nat,X1: list_P559422087at_nat] : ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(list_P559422087at_nat,nat,size_s1990949619at_nat,vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,X0),X1))),vAPP(list_P559422087at_nat,nat,size_s1990949619at_nat,X1)) )
| ~ spl155_2
| ~ spl155_100 ),
inference(trivial_inequality_removal,[],[f3473]) ).
thf(f3473,plain,
( ! [X0: product_prod_nat_nat,X1: list_P559422087at_nat] :
( ( $true != $true )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(list_P559422087at_nat,nat,size_s1990949619at_nat,vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,X0),X1))),vAPP(list_P559422087at_nat,nat,size_s1990949619at_nat,X1)) ) )
| ~ spl155_2
| ~ spl155_100 ),
inference(superposition,[],[f3437,f2740]) ).
thf(f14472,plain,
( spl155_573
| ~ spl155_106
| ~ spl155_551 ),
inference(avatar_split_clause,[],[f14045,f12930,f3492,f14470]) ).
thf(f3492,plain,
( spl155_106
<=> ! [X0: set_Pr1986765409at_nat] : ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_106])]) ).
thf(f12930,plain,
( spl155_551
<=> ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1)),edges)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_551])]) ).
thf(f14045,plain,
( ! [X0: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,X0),edges)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),X0) ) )
| ~ spl155_106
| ~ spl155_551 ),
inference(superposition,[],[f12931,f3493]) ).
thf(f3493,plain,
( ! [X0: set_Pr1986765409at_nat] : ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X0) = X0 )
| ~ spl155_106 ),
inference(avatar_component_clause,[],[f3492]) ).
thf(f12931,plain,
( ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1)),edges)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),X0) ) )
| ~ spl155_551 ),
inference(avatar_component_clause,[],[f12930]) ).
thf(f14468,plain,
( spl155_572
| ~ spl155_9
| ~ spl155_120 ),
inference(avatar_split_clause,[],[f3696,f3636,f2806,f14466]) ).
thf(f14466,plain,
( spl155_572
<=> ! [X0: set_Pr1986765409at_nat,X1: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK17,X0),X1)),X0) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_572])]) ).
thf(f3696,plain,
( ! [X0: set_Pr1986765409at_nat,X1: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK17,X0),X1)),X0) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) ) )
| ~ spl155_9
| ~ spl155_120 ),
inference(trivial_inequality_removal,[],[f3693]) ).
thf(f3693,plain,
( ! [X0: set_Pr1986765409at_nat,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK17,X0),X1)),X0) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) ) )
| ~ spl155_9
| ~ spl155_120 ),
inference(superposition,[],[f3637,f2807]) ).
thf(f14087,plain,
( spl155_571
| ~ spl155_68
| ~ spl155_173 ),
inference(avatar_split_clause,[],[f4783,f4743,f3209,f14085]) ).
thf(f14085,plain,
( spl155_571
<=> ! [X0: set_Pr1986765409at_nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK28,X0),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_571])]) ).
thf(f3209,plain,
( spl155_68
<=> ! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_68])]) ).
thf(f4783,plain,
( ! [X0: set_Pr1986765409at_nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK28,X0),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0))),X0) )
| ~ spl155_68
| ~ spl155_173 ),
inference(trivial_inequality_removal,[],[f4766]) ).
thf(f4766,plain,
( ! [X0: set_Pr1986765409at_nat] :
( ( $true != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK28,X0),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0))),X0) ) )
| ~ spl155_68
| ~ spl155_173 ),
inference(superposition,[],[f4744,f3210]) ).
thf(f3210,plain,
( ! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),X0) )
| ~ spl155_68 ),
inference(avatar_component_clause,[],[f3209]) ).
thf(f14083,plain,
( spl155_570
| ~ spl155_68
| ~ spl155_172 ),
inference(avatar_split_clause,[],[f4763,f4739,f3209,f14081]) ).
thf(f14081,plain,
( spl155_570
<=> ! [X0: set_nat] : ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK27,X0),vAPP(set_nat,nat,finite_card_nat,X0))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_570])]) ).
thf(f4763,plain,
( ! [X0: set_nat] : ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK27,X0),vAPP(set_nat,nat,finite_card_nat,X0))),X0) )
| ~ spl155_68
| ~ spl155_172 ),
inference(trivial_inequality_removal,[],[f4746]) ).
thf(f4746,plain,
( ! [X0: set_nat] :
( ( $true != $true )
| ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK27,X0),vAPP(set_nat,nat,finite_card_nat,X0))),X0) ) )
| ~ spl155_68
| ~ spl155_172 ),
inference(superposition,[],[f4740,f3210]) ).
thf(f14044,plain,
( spl155_569
| ~ spl155_71
| ~ spl155_164 ),
inference(avatar_split_clause,[],[f4637,f4483,f3223,f14042]) ).
thf(f14042,plain,
( spl155_569
<=> ! [X0: set_Pr1986765409at_nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),edges)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_569])]) ).
thf(f3223,plain,
( spl155_71
<=> ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),edges),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_71])]) ).
thf(f4637,plain,
( ! [X0: set_Pr1986765409at_nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),edges)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p)) )
| ~ spl155_71
| ~ spl155_164 ),
inference(trivial_inequality_removal,[],[f4620]) ).
thf(f4620,plain,
( ! [X0: set_Pr1986765409at_nat] :
( ( $true != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),edges)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p)) ) )
| ~ spl155_71
| ~ spl155_164 ),
inference(superposition,[],[f4484,f3225]) ).
thf(f3225,plain,
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),edges),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p)) )
| ~ spl155_71 ),
inference(avatar_component_clause,[],[f3223]) ).
thf(f14040,plain,
( spl155_568
| ~ spl155_71
| ~ spl155_163 ),
inference(avatar_split_clause,[],[f4609,f4479,f3223,f14038]) ).
thf(f14038,plain,
( spl155_568
<=> ! [X0: set_Pr1986765409at_nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,edges),X0)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_568])]) ).
thf(f4609,plain,
( ! [X0: set_Pr1986765409at_nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,edges),X0)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p)) )
| ~ spl155_71
| ~ spl155_163 ),
inference(trivial_inequality_removal,[],[f4592]) ).
thf(f4592,plain,
( ! [X0: set_Pr1986765409at_nat] :
( ( $true != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,edges),X0)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p)) ) )
| ~ spl155_71
| ~ spl155_163 ),
inference(superposition,[],[f4480,f3225]) ).
thf(f14036,plain,
( spl155_567
| ~ spl155_2
| ~ spl155_90 ),
inference(avatar_split_clause,[],[f3376,f3367,f2739,f14034]) ).
thf(f14034,plain,
( spl155_567
<=> ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X1) )
| ( $false = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_567])]) ).
thf(f3367,plain,
( spl155_90
<=> ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X1) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X1),X0) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_90])]) ).
thf(f3376,plain,
( ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X1) )
| ( $false = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X1) ) )
| ~ spl155_2
| ~ spl155_90 ),
inference(trivial_inequality_removal,[],[f3375]) ).
thf(f3375,plain,
( ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X1) )
| ( $false = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X1) ) )
| ~ spl155_2
| ~ spl155_90 ),
inference(superposition,[],[f3368,f2740]) ).
thf(f3368,plain,
( ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X1),X0) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X1) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) ) )
| ~ spl155_90 ),
inference(avatar_component_clause,[],[f3367]) ).
thf(f14032,plain,
spl155_566,
inference(avatar_split_clause,[],[f2563,f14030]) ).
thf(f14030,plain,
( spl155_566
<=> ! [X2: nat,X0: nat,X1: list_P559422087at_nat] :
( ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),vAPP($o,sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat))),sK85,vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X2))),X2),X1),X0)),vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),vAPP($o,sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat))),sK86,vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X2))),X2),X1),X0))),vAPP(nat,list_P559422087at_nat,vAPP(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat)),vAPP($o,sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat))),sK87,vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X2))),X2),X1),X0)) = X1 )
| ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2) )
| ( X0 != X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_566])]) ).
thf(f2563,plain,
! [X2: nat,X0: nat,X1: list_P559422087at_nat] :
( ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),vAPP($o,sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat))),sK85,vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X2))),X2),X1),X0)),vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),vAPP($o,sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat))),sK86,vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X2))),X2),X1),X0))),vAPP(nat,list_P559422087at_nat,vAPP(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat)),vAPP($o,sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat))),sK87,vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X2))),X2),X1),X0)) = X1 )
| ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2) )
| ( X0 != X2 ) ),
inference(equality_proxy_clausification,[],[f2562]) ).
thf(f2562,plain,
! [X2: nat,X0: nat,X1: list_P559422087at_nat] :
( ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),vAPP($o,sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat))),sK85,vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X2))),X2),X1),X0)),vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),vAPP($o,sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat))),sK86,vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X2))),X2),X1),X0))),vAPP(nat,list_P559422087at_nat,vAPP(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat)),vAPP($o,sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat))),sK87,vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X2))),X2),X1),X0)) = X1 )
| ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X2) ) ),
inference(not_proxy_clausification,[],[f2558]) ).
thf(f2558,plain,
! [X2: nat,X0: nat,X1: list_P559422087at_nat] :
( ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),vAPP($o,sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat))),sK85,vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X2))),X2),X1),X0)),vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),vAPP($o,sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat))),sK86,vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X2))),X2),X1),X0))),vAPP(nat,list_P559422087at_nat,vAPP(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat)),vAPP($o,sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat))),sK87,vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X2))),X2),X1),X0)) = X1 )
| ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2) )
| ( $true = vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X2)) ) ),
inference(binary_proxy_clausification,[],[f2528]) ).
thf(f2528,plain,
! [X2: nat,X0: nat,X1: list_P559422087at_nat] :
( ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),vAPP($o,sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat))),sK85,vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X2))),X2),X1),X0)),vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),vAPP($o,sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat))),sK86,vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X2))),X2),X1),X0))),vAPP(nat,list_P559422087at_nat,vAPP(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat)),vAPP($o,sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat))),sK87,vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X2))),X2),X1),X0)) = X1 )
| ( vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2) != vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X2)) ) ),
inference(equality_resolution,[],[f2005]) ).
thf(f2005,plain,
! [X2: nat,X3: $o,X0: nat,X1: list_P559422087at_nat] :
( ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),vAPP($o,sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat))),sK85,X3),X2),X1),X0)),vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),vAPP($o,sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat))),sK86,X3),X2),X1),X0))),vAPP(nat,list_P559422087at_nat,vAPP(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat)),vAPP($o,sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat))),sK87,X3),X2),X1),X0)) = X1 )
| ( vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X2)) != X3 )
| ( vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2) != X3 ) ),
inference(cnf_transformation,[],[f1548]) ).
thf(f1548,plain,
! [X0: nat,X1: list_P559422087at_nat,X2: nat,X3: $o] :
( ( ( vAPP($o,$o,vNOT,vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),vAPP($o,sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat))),sK85,X3),X2),X1),X0))),vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),vAPP($o,sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat))),sK85,X3),X2),X1),X0)),vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),vAPP($o,sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat))),sK86,X3),X2),X1),X0))),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)))),vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),vAPP($o,sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat))),sK86,X3),X2),X1),X0)),vAPP(nat,list_P559422087at_nat,vAPP(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat)),vAPP($o,sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat))),sK87,X3),X2),X1),X0)),X2))) != X3 )
& ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),vAPP($o,sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat))),sK85,X3),X2),X1),X0)),vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),vAPP($o,sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat))),sK86,X3),X2),X1),X0))),vAPP(nat,list_P559422087at_nat,vAPP(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat)),vAPP($o,sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat))),sK87,X3),X2),X1),X0)) = X1 ) )
| ( ( vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X2)) != X3 )
& ( nil_Pr1308055047at_nat = X1 ) )
| ( vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2) != X3 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK85,sK86,sK87])],[f1338,f1547]) ).
thf(f1547,plain,
! [X0: nat,X1: list_P559422087at_nat,X2: nat,X3: $o] :
( ? [X4: nat,X5: nat,X6: list_P559422087at_nat] :
( ( vAPP($o,$o,vNOT,vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X4)),vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X4),X5)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)))),vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X5),X6),X2))) != X3 )
& ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X4),X5)),X6) = X1 ) )
=> ( ( vAPP($o,$o,vNOT,vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),vAPP($o,sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat))),sK85,X3),X2),X1),X0))),vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),vAPP($o,sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat))),sK85,X3),X2),X1),X0)),vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),vAPP($o,sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat))),sK86,X3),X2),X1),X0))),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)))),vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),vAPP($o,sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat))),sK86,X3),X2),X1),X0)),vAPP(nat,list_P559422087at_nat,vAPP(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat)),vAPP($o,sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat))),sK87,X3),X2),X1),X0)),X2))) != X3 )
& ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),vAPP($o,sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat))),sK85,X3),X2),X1),X0)),vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),vAPP($o,sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat))),sK86,X3),X2),X1),X0))),vAPP(nat,list_P559422087at_nat,vAPP(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat)),vAPP($o,sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat))),sK87,X3),X2),X1),X0)) = X1 ) ) ),
introduced(choice_axiom,[]) ).
thf(f1338,plain,
! [X0: nat,X1: list_P559422087at_nat,X2: nat,X3: $o] :
( ? [X4: nat,X5: nat,X6: list_P559422087at_nat] :
( ( vAPP($o,$o,vNOT,vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X4)),vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X4),X5)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)))),vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X5),X6),X2))) != X3 )
& ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X4),X5)),X6) = X1 ) )
| ( ( vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X2)) != X3 )
& ( nil_Pr1308055047at_nat = X1 ) )
| ( vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2) != X3 ) ),
inference(flattening,[],[f1337]) ).
thf(f1337,plain,
! [X0: nat,X1: list_P559422087at_nat,X2: nat,X3: $o] :
( ? [X4: nat,X5: nat,X6: list_P559422087at_nat] :
( ( vAPP($o,$o,vNOT,vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X4)),vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X4),X5)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)))),vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X5),X6),X2))) != X3 )
& ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X4),X5)),X6) = X1 ) )
| ( ( vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X2)) != X3 )
& ( nil_Pr1308055047at_nat = X1 ) )
| ( vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2) != X3 ) ),
inference(ennf_transformation,[],[f919]) ).
thf(f919,plain,
! [X0: nat,X1: list_P559422087at_nat,X2: nat,X3: $o] :
( ( vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2) = X3 )
=> ( ( ( nil_Pr1308055047at_nat = X1 )
=> ( vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X2)) = X3 ) )
=> ~ ! [X4: nat,X5: nat,X6: list_P559422087at_nat] :
( ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X4),X5)),X6) = X1 )
=> ( vAPP($o,$o,vNOT,vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X4)),vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X4),X5)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)))),vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X5),X6),X2))) = X3 ) ) ) ),
inference(fool_elimination,[],[f918]) ).
thf(f918,plain,
! [X0: nat,X1: list_P559422087at_nat,X2: nat,X3: $o] :
( ( vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2) = X3 )
=> ( ( ( nil_Pr1308055047at_nat = X1 )
=> ( X3
= ( X0 != X2 ) ) )
=> ~ ! [X4: nat,X5: nat,X6: list_P559422087at_nat] :
( ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X4),X5)),X6) = X1 )
=> ( X3
= ( ~ ( vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X5),X6),X2)
& vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X4),X5)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c))
& ( X0 = X4 ) ) ) ) ) ) ),
inference(rectify,[],[f352]) ).
thf(f352,axiom,
! [X5: nat,X65: list_P559422087at_nat,X66: nat,X21: $o] :
( ( vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X5),X65),X66) = X21 )
=> ( ( ( nil_Pr1308055047at_nat = X65 )
=> ( X21
= ( X5 != X66 ) ) )
=> ~ ! [X4: nat,X26: nat,X67: list_P559422087at_nat] :
( ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X4),X26)),X67) = X65 )
=> ( X21
= ( ~ ( vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X26),X67),X66)
& vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X4),X26)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c))
& ( X4 = X5 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_351_isPath_Oelims_I1_J) ).
thf(f14028,plain,
spl155_565,
inference(avatar_split_clause,[],[f2561,f14026]) ).
thf(f14026,plain,
( spl155_565
<=> ! [X2: nat,X0: nat,X1: list_P559422087at_nat] :
( ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),vAPP($o,sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat))),sK85,vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X2))),X2),X1),X0)),vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),vAPP($o,sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat))),sK86,vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X2))),X2),X1),X0))),vAPP(nat,list_P559422087at_nat,vAPP(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat)),vAPP($o,sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat))),sK87,vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X2))),X2),X1),X0)) = X1 )
| ( $false = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2) )
| ( X0 = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_565])]) ).
thf(f2561,plain,
! [X2: nat,X0: nat,X1: list_P559422087at_nat] :
( ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),vAPP($o,sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat))),sK85,vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X2))),X2),X1),X0)),vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),vAPP($o,sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat))),sK86,vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X2))),X2),X1),X0))),vAPP(nat,list_P559422087at_nat,vAPP(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat)),vAPP($o,sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat))),sK87,vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X2))),X2),X1),X0)) = X1 )
| ( $false = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2) )
| ( X0 = X2 ) ),
inference(equality_proxy_clausification,[],[f2560]) ).
thf(f2560,plain,
! [X2: nat,X0: nat,X1: list_P559422087at_nat] :
( ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),vAPP($o,sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat))),sK85,vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X2))),X2),X1),X0)),vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),vAPP($o,sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat))),sK86,vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X2))),X2),X1),X0))),vAPP(nat,list_P559422087at_nat,vAPP(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat)),vAPP($o,sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat))),sK87,vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X2))),X2),X1),X0)) = X1 )
| ( $false = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X2) ) ),
inference(not_proxy_clausification,[],[f2559]) ).
thf(f2559,plain,
! [X2: nat,X0: nat,X1: list_P559422087at_nat] :
( ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),vAPP($o,sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat))),sK85,vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X2))),X2),X1),X0)),vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),vAPP($o,sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat))),sK86,vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X2))),X2),X1),X0))),vAPP(nat,list_P559422087at_nat,vAPP(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat)),vAPP($o,sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat))),sK87,vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X2))),X2),X1),X0)) = X1 )
| ( $false = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2) )
| ( $false = vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X2)) ) ),
inference(binary_proxy_clausification,[],[f2528]) ).
thf(f13164,plain,
( spl155_564
| ~ spl155_87
| ~ spl155_155 ),
inference(avatar_split_clause,[],[f4381,f4326,f3293,f13162]) ).
thf(f13162,plain,
( spl155_564
<=> ! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X1),X0) = X0 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_564])]) ).
thf(f3293,plain,
( spl155_87
<=> ! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X1),X0) = X0 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_87])]) ).
thf(f4381,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X1),X0) = X0 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X1),X0) ) )
| ~ spl155_87
| ~ spl155_155 ),
inference(trivial_inequality_removal,[],[f4332]) ).
thf(f4332,plain,
( ! [X0: nat,X1: nat] :
( ( $true != $true )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X1),X0) = X0 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X1),X0) ) )
| ~ spl155_87
| ~ spl155_155 ),
inference(superposition,[],[f3294,f4327]) ).
thf(f3294,plain,
( ! [X0: nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),X1) )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X1),X0) = X0 ) )
| ~ spl155_87 ),
inference(avatar_component_clause,[],[f3293]) ).
thf(f13160,plain,
( spl155_563
| ~ spl155_86
| ~ spl155_155 ),
inference(avatar_split_clause,[],[f4380,f4326,f3289,f13158]) ).
thf(f13158,plain,
( spl155_563
<=> ! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X1) = X0 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_563])]) ).
thf(f3289,plain,
( spl155_86
<=> ! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X1) = X0 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_86])]) ).
thf(f4380,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X1) = X0 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X1),X0) ) )
| ~ spl155_86
| ~ spl155_155 ),
inference(trivial_inequality_removal,[],[f4333]) ).
thf(f4333,plain,
( ! [X0: nat,X1: nat] :
( ( $true != $true )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X1) = X0 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X1),X0) ) )
| ~ spl155_86
| ~ spl155_155 ),
inference(superposition,[],[f3290,f4327]) ).
thf(f3290,plain,
( ! [X0: nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),X1) )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X1) = X0 ) )
| ~ spl155_86 ),
inference(avatar_component_clause,[],[f3289]) ).
thf(f13156,plain,
( spl155_562
| ~ spl155_2
| ~ spl155_89 ),
inference(avatar_split_clause,[],[f3360,f3301,f2739,f13154]) ).
thf(f13154,plain,
( spl155_562
<=> ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1) = X0 )
| ( $false = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_562])]) ).
thf(f3301,plain,
( spl155_89
<=> ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1) = X0 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_89])]) ).
thf(f3360,plain,
( ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1) = X0 )
| ( $false = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X1) ) )
| ~ spl155_2
| ~ spl155_89 ),
inference(trivial_inequality_removal,[],[f3359]) ).
thf(f3359,plain,
( ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true != $true )
| ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1) = X0 )
| ( $false = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X1) ) )
| ~ spl155_2
| ~ spl155_89 ),
inference(superposition,[],[f3302,f2740]) ).
thf(f3302,plain,
( ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X1) )
| ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1) = X0 ) )
| ~ spl155_89 ),
inference(avatar_component_clause,[],[f3301]) ).
thf(f13152,plain,
( spl155_561
| ~ spl155_2
| ~ spl155_88 ),
inference(avatar_split_clause,[],[f3348,f3297,f2739,f13150]) ).
thf(f13150,plain,
( spl155_561
<=> ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),X0) = X0 )
| ( $false = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_561])]) ).
thf(f3297,plain,
( spl155_88
<=> ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),X0) = X0 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_88])]) ).
thf(f3348,plain,
( ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),X0) = X0 )
| ( $false = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X1) ) )
| ~ spl155_2
| ~ spl155_88 ),
inference(trivial_inequality_removal,[],[f3347]) ).
thf(f3347,plain,
( ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true != $true )
| ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),X0) = X0 )
| ( $false = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X1) ) )
| ~ spl155_2
| ~ spl155_88 ),
inference(superposition,[],[f3298,f2740]) ).
thf(f3298,plain,
( ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X1) )
| ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),X0) = X0 ) )
| ~ spl155_88 ),
inference(avatar_component_clause,[],[f3297]) ).
thf(f13148,plain,
( spl155_560
| ~ spl155_2
| ~ spl155_87 ),
inference(avatar_split_clause,[],[f3338,f3293,f2739,f13146]) ).
thf(f13146,plain,
( spl155_560
<=> ! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X1),X0) = X0 )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_560])]) ).
thf(f3338,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X1),X0) = X0 )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),X1) ) )
| ~ spl155_2
| ~ spl155_87 ),
inference(trivial_inequality_removal,[],[f3337]) ).
thf(f3337,plain,
( ! [X0: nat,X1: nat] :
( ( $true != $true )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X1),X0) = X0 )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),X1) ) )
| ~ spl155_2
| ~ spl155_87 ),
inference(superposition,[],[f3294,f2740]) ).
thf(f13144,plain,
( spl155_559
| ~ spl155_2
| ~ spl155_86 ),
inference(avatar_split_clause,[],[f3330,f3289,f2739,f13142]) ).
thf(f13142,plain,
( spl155_559
<=> ! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X1) = X0 )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_559])]) ).
thf(f3330,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X1) = X0 )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),X1) ) )
| ~ spl155_2
| ~ spl155_86 ),
inference(trivial_inequality_removal,[],[f3329]) ).
thf(f3329,plain,
( ! [X0: nat,X1: nat] :
( ( $true != $true )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X1) = X0 )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),X1) ) )
| ~ spl155_2
| ~ spl155_86 ),
inference(superposition,[],[f3290,f2740]) ).
thf(f13140,plain,
( spl155_558
| ~ spl155_2
| ~ spl155_85 ),
inference(avatar_split_clause,[],[f3322,f3285,f2739,f13138]) ).
thf(f13138,plain,
( spl155_558
<=> ! [X0: set_nat,X1: set_nat] :
( ( vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X1) = X0 )
| ( $false = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_558])]) ).
thf(f3285,plain,
( spl155_85
<=> ! [X0: set_nat,X1: set_nat] :
( ( vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X1) = X0 )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_85])]) ).
thf(f3322,plain,
( ! [X0: set_nat,X1: set_nat] :
( ( vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X1) = X0 )
| ( $false = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),X1) ) )
| ~ spl155_2
| ~ spl155_85 ),
inference(trivial_inequality_removal,[],[f3321]) ).
thf(f3321,plain,
( ! [X0: set_nat,X1: set_nat] :
( ( $true != $true )
| ( vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X1) = X0 )
| ( $false = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),X1) ) )
| ~ spl155_2
| ~ spl155_85 ),
inference(superposition,[],[f3286,f2740]) ).
thf(f3286,plain,
( ! [X0: set_nat,X1: set_nat] :
( ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),X1) )
| ( vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X1) = X0 ) )
| ~ spl155_85 ),
inference(avatar_component_clause,[],[f3285]) ).
thf(f13136,plain,
( spl155_557
| ~ spl155_349
| ~ spl155_517 ),
inference(avatar_split_clause,[],[f12290,f11868,f7504,f13134]) ).
thf(f13134,plain,
( spl155_557
<=> ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1)),edges)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_557])]) ).
thf(f7504,plain,
( spl155_349
<=> ! [X0: product_prod_nat_nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),edges) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_349])]) ).
thf(f11868,plain,
( spl155_517
<=> ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),X1) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1)),edges)),edges) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_517])]) ).
thf(f12290,plain,
( ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1)),edges)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),X1) ) )
| ~ spl155_349
| ~ spl155_517 ),
inference(trivial_inequality_removal,[],[f12283]) ).
thf(f12283,plain,
( ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1)),edges)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),X1) ) )
| ~ spl155_349
| ~ spl155_517 ),
inference(superposition,[],[f7505,f11869]) ).
thf(f11869,plain,
( ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1)),edges)),edges) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),X1) ) )
| ~ spl155_517 ),
inference(avatar_component_clause,[],[f11868]) ).
thf(f7505,plain,
( ! [X0: product_prod_nat_nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),edges) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p)) ) )
| ~ spl155_349 ),
inference(avatar_component_clause,[],[f7504]) ).
thf(f13132,plain,
( spl155_556
| ~ spl155_2
| ~ spl155_84 ),
inference(avatar_split_clause,[],[f3314,f3281,f2739,f13130]) ).
thf(f13130,plain,
( spl155_556
<=> ! [X0: set_nat,X1: set_nat] :
( ( vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),X0) = X0 )
| ( $false = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_556])]) ).
thf(f3281,plain,
( spl155_84
<=> ! [X0: set_nat,X1: set_nat] :
( ( vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),X0) = X0 )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_84])]) ).
thf(f3314,plain,
( ! [X0: set_nat,X1: set_nat] :
( ( vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),X0) = X0 )
| ( $false = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),X1) ) )
| ~ spl155_2
| ~ spl155_84 ),
inference(trivial_inequality_removal,[],[f3313]) ).
thf(f3313,plain,
( ! [X0: set_nat,X1: set_nat] :
( ( $true != $true )
| ( vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),X0) = X0 )
| ( $false = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),X1) ) )
| ~ spl155_2
| ~ spl155_84 ),
inference(superposition,[],[f3282,f2740]) ).
thf(f3282,plain,
( ! [X0: set_nat,X1: set_nat] :
( ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),X1) )
| ( vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),X0) = X0 ) )
| ~ spl155_84 ),
inference(avatar_component_clause,[],[f3281]) ).
thf(f13080,plain,
( spl155_555
| ~ spl155_3
| ~ spl155_71
| ~ spl155_174 ),
inference(avatar_split_clause,[],[f4817,f4786,f3223,f2771,f13077]) ).
thf(f13077,plain,
( spl155_555
<=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,edges)),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_555])]) ).
thf(f2771,plain,
( spl155_3
<=> ! [X0: list_P559422087at_nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_3])]) ).
thf(f4817,plain,
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,edges)),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p))) )
| ~ spl155_3
| ~ spl155_71
| ~ spl155_174 ),
inference(trivial_inequality_removal,[],[f4816]) ).
thf(f4816,plain,
( ( $true != $true )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,edges)),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p))) )
| ~ spl155_3
| ~ spl155_71
| ~ spl155_174 ),
inference(forward_demodulation,[],[f4811,f2772]) ).
thf(f2772,plain,
( ! [X0: list_P559422087at_nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X0)) )
| ~ spl155_3 ),
inference(avatar_component_clause,[],[f2771]) ).
thf(f4811,plain,
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,edges)),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p))) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p)) )
| ~ spl155_71
| ~ spl155_174 ),
inference(trivial_inequality_removal,[],[f4794]) ).
thf(f4794,plain,
( ( $true != $true )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,edges)),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p))) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p)) )
| ~ spl155_71
| ~ spl155_174 ),
inference(superposition,[],[f4787,f3225]) ).
thf(f13071,plain,
( ~ spl155_554
| spl155_242
| ~ spl155_71
| ~ spl155_158 ),
inference(avatar_split_clause,[],[f4451,f4394,f3223,f6042,f13068]) ).
thf(f13068,plain,
( spl155_554
<=> ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p)),edges) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_554])]) ).
thf(f6042,plain,
( spl155_242
<=> ( edges = vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_242])]) ).
thf(f4451,plain,
( ( edges = vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p)),edges) )
| ~ spl155_71
| ~ spl155_158 ),
inference(trivial_inequality_removal,[],[f4434]) ).
thf(f4434,plain,
( ( $true != $true )
| ( edges = vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p)),edges) )
| ~ spl155_71
| ~ spl155_158 ),
inference(superposition,[],[f4395,f3225]) ).
thf(f13064,plain,
( spl155_553
| ~ spl155_2
| ~ spl155_66 ),
inference(avatar_split_clause,[],[f3203,f3199,f2739,f13062]) ).
thf(f13062,plain,
( spl155_553
<=> ! [X2: nat,X0: nat,X1: list_P559422087at_nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X2),vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),sK33,X0),X1),X2))),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) )
| ( vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),sK32,X0),X1),X2) != X2 )
| ( nil_Pr1308055047at_nat = X1 )
| ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X2),X1),X0) )
| ( $false = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),sK33,X0),X1),X2)),vAPP(nat,list_P559422087at_nat,vAPP(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat)),sK34,X0),X1),X2)),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_553])]) ).
thf(f3199,plain,
( spl155_66
<=> ! [X2: nat,X0: nat,X1: list_P559422087at_nat] :
( ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),sK33,X2),X1),X0)),vAPP(nat,list_P559422087at_nat,vAPP(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat)),sK34,X2),X1),X0)),X2) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X0),vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),sK33,X2),X1),X0))),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) )
| ( vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),sK32,X2),X1),X0) != X0 )
| ( nil_Pr1308055047at_nat = X1 )
| ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_66])]) ).
thf(f3203,plain,
( ! [X2: nat,X0: nat,X1: list_P559422087at_nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X2),vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),sK33,X0),X1),X2))),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) )
| ( vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),sK32,X0),X1),X2) != X2 )
| ( nil_Pr1308055047at_nat = X1 )
| ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X2),X1),X0) )
| ( $false = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),sK33,X0),X1),X2)),vAPP(nat,list_P559422087at_nat,vAPP(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat)),sK34,X0),X1),X2)),X0) ) )
| ~ spl155_2
| ~ spl155_66 ),
inference(trivial_inequality_removal,[],[f3202]) ).
thf(f3202,plain,
( ! [X2: nat,X0: nat,X1: list_P559422087at_nat] :
( ( $true != $true )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X2),vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),sK33,X0),X1),X2))),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) )
| ( vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),sK32,X0),X1),X2) != X2 )
| ( nil_Pr1308055047at_nat = X1 )
| ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X2),X1),X0) )
| ( $false = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),sK33,X0),X1),X2)),vAPP(nat,list_P559422087at_nat,vAPP(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat)),sK34,X0),X1),X2)),X0) ) )
| ~ spl155_2
| ~ spl155_66 ),
inference(superposition,[],[f3200,f2740]) ).
thf(f3200,plain,
( ! [X2: nat,X0: nat,X1: list_P559422087at_nat] :
( ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),sK33,X2),X1),X0)),vAPP(nat,list_P559422087at_nat,vAPP(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat)),sK34,X2),X1),X0)),X2) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X0),vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),sK33,X2),X1),X0))),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) )
| ( vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),sK32,X2),X1),X0) != X0 )
| ( nil_Pr1308055047at_nat = X1 )
| ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2) ) )
| ~ spl155_66 ),
inference(avatar_component_clause,[],[f3199]) ).
thf(f13058,plain,
( spl155_552
| ~ spl155_2
| ~ spl155_65 ),
inference(avatar_split_clause,[],[f3197,f3193,f2739,f13056]) ).
thf(f13056,plain,
( spl155_552
<=> ! [X0: nat,X1: list_P559422087at_nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X0),vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),sK33,X0),X1),X0))),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) )
| ( vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),sK32,X0),X1),X0) != X0 )
| ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X0) )
| ( $false = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),sK33,X0),X1),X0)),vAPP(nat,list_P559422087at_nat,vAPP(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat)),sK34,X0),X1),X0)),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_552])]) ).
thf(f3193,plain,
( spl155_65
<=> ! [X2: nat,X1: list_P559422087at_nat] :
( ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),sK33,X2),X1),X2)),vAPP(nat,list_P559422087at_nat,vAPP(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat)),sK34,X2),X1),X2)),X2) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X2),vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),sK33,X2),X1),X2))),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) )
| ( vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),sK32,X2),X1),X2) != X2 )
| ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X2),X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_65])]) ).
thf(f3197,plain,
( ! [X0: nat,X1: list_P559422087at_nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X0),vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),sK33,X0),X1),X0))),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) )
| ( vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),sK32,X0),X1),X0) != X0 )
| ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X0) )
| ( $false = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),sK33,X0),X1),X0)),vAPP(nat,list_P559422087at_nat,vAPP(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat)),sK34,X0),X1),X0)),X0) ) )
| ~ spl155_2
| ~ spl155_65 ),
inference(trivial_inequality_removal,[],[f3196]) ).
thf(f3196,plain,
( ! [X0: nat,X1: list_P559422087at_nat] :
( ( $true != $true )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X0),vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),sK33,X0),X1),X0))),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) )
| ( vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),sK32,X0),X1),X0) != X0 )
| ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X0) )
| ( $false = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),sK33,X0),X1),X0)),vAPP(nat,list_P559422087at_nat,vAPP(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat)),sK34,X0),X1),X0)),X0) ) )
| ~ spl155_2
| ~ spl155_65 ),
inference(superposition,[],[f3194,f2740]) ).
thf(f3194,plain,
( ! [X2: nat,X1: list_P559422087at_nat] :
( ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),sK33,X2),X1),X2)),vAPP(nat,list_P559422087at_nat,vAPP(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat)),sK34,X2),X1),X2)),X2) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X2),vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),sK33,X2),X1),X2))),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) )
| ( vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),sK32,X2),X1),X2) != X2 )
| ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X2),X1),X2) ) )
| ~ spl155_65 ),
inference(avatar_component_clause,[],[f3193]) ).
thf(f12932,plain,
( spl155_551
| ~ spl155_349
| ~ spl155_511 ),
inference(avatar_split_clause,[],[f12070,f11358,f7504,f12930]) ).
thf(f11358,plain,
( spl155_511
<=> ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),X0) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1)),edges)),edges) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_511])]) ).
thf(f12070,plain,
( ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1)),edges)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),X0) ) )
| ~ spl155_349
| ~ spl155_511 ),
inference(trivial_inequality_removal,[],[f12063]) ).
thf(f12063,plain,
( ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1)),edges)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),X0) ) )
| ~ spl155_349
| ~ spl155_511 ),
inference(superposition,[],[f7505,f11359]) ).
thf(f11359,plain,
( ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1)),edges)),edges) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),X0) ) )
| ~ spl155_511 ),
inference(avatar_component_clause,[],[f11358]) ).
thf(f12928,plain,
( spl155_550
| ~ spl155_132
| ~ spl155_149 ),
inference(avatar_split_clause,[],[f4292,f4212,f3810,f12926]) ).
thf(f12926,plain,
( spl155_550
<=> ! [X0: nat,X3: nat,X2: nat,X1: nat > $o] :
( ( $true = vAPP(nat,$o,X1,vAPP(sTfun(nat,$o),nat,sK60,X1)) )
| ( $true != vAPP(nat,$o,X1,X2) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP5,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK61,X0),X1)),X3),X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP4,X0),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK61,X0),X1)),X3) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP3,X3),X0),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK61,X0),X1)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP2,X0),X3),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK61,X0),X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_550])]) ).
thf(f3810,plain,
( spl155_132
<=> ! [X2: nat,X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK60,X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK61,X2),X0)),X2) )
| ( $true != vAPP(nat,$o,X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_132])]) ).
thf(f4212,plain,
( spl155_149
<=> ! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X2),X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP5,X2),X1),X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP4,X0),X2),X1) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP3,X1),X0),X2) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP2,X0),X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_149])]) ).
thf(f4292,plain,
( ! [X2: nat,X3: nat,X0: nat,X1: nat > $o] :
( ( $true = vAPP(nat,$o,X1,vAPP(sTfun(nat,$o),nat,sK60,X1)) )
| ( $true != vAPP(nat,$o,X1,X2) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP5,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK61,X0),X1)),X3),X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP4,X0),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK61,X0),X1)),X3) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP3,X3),X0),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK61,X0),X1)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP2,X0),X3),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK61,X0),X1)) ) )
| ~ spl155_132
| ~ spl155_149 ),
inference(trivial_inequality_removal,[],[f4215]) ).
thf(f4215,plain,
( ! [X2: nat,X3: nat,X0: nat,X1: nat > $o] :
( ( $true != $true )
| ( $true = vAPP(nat,$o,X1,vAPP(sTfun(nat,$o),nat,sK60,X1)) )
| ( $true != vAPP(nat,$o,X1,X2) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP5,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK61,X0),X1)),X3),X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP4,X0),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK61,X0),X1)),X3) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP3,X3),X0),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK61,X0),X1)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP2,X0),X3),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK61,X0),X1)) ) )
| ~ spl155_132
| ~ spl155_149 ),
inference(superposition,[],[f3811,f4213]) ).
thf(f4213,plain,
( ! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X2),X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP5,X2),X1),X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP4,X0),X2),X1) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP3,X1),X0),X2) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP2,X0),X1),X2) ) )
| ~ spl155_149 ),
inference(avatar_component_clause,[],[f4212]) ).
thf(f3811,plain,
( ! [X2: nat,X0: nat > $o,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK61,X2),X0)),X2) )
| ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK60,X0)) )
| ( $true != vAPP(nat,$o,X0,X1) ) )
| ~ spl155_132 ),
inference(avatar_component_clause,[],[f3810]) ).
thf(f12887,plain,
( spl155_549
| ~ spl155_100
| ~ spl155_149 ),
inference(avatar_split_clause,[],[f4281,f4212,f3436,f12885]) ).
thf(f12885,plain,
( spl155_549
<=> ! [X2: nat,X0: product_prod_nat_nat,X1: list_P559422087at_nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP5,vAPP(list_P559422087at_nat,nat,size_s1990949619at_nat,vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,X0),X1))),X2),vAPP(list_P559422087at_nat,nat,size_s1990949619at_nat,X1)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP4,vAPP(list_P559422087at_nat,nat,size_s1990949619at_nat,X1)),vAPP(list_P559422087at_nat,nat,size_s1990949619at_nat,vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,X0),X1))),X2) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP3,X2),vAPP(list_P559422087at_nat,nat,size_s1990949619at_nat,X1)),vAPP(list_P559422087at_nat,nat,size_s1990949619at_nat,vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,X0),X1))) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP2,vAPP(list_P559422087at_nat,nat,size_s1990949619at_nat,X1)),X2),vAPP(list_P559422087at_nat,nat,size_s1990949619at_nat,vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,X0),X1))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_549])]) ).
thf(f4281,plain,
( ! [X2: nat,X0: product_prod_nat_nat,X1: list_P559422087at_nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP5,vAPP(list_P559422087at_nat,nat,size_s1990949619at_nat,vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,X0),X1))),X2),vAPP(list_P559422087at_nat,nat,size_s1990949619at_nat,X1)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP4,vAPP(list_P559422087at_nat,nat,size_s1990949619at_nat,X1)),vAPP(list_P559422087at_nat,nat,size_s1990949619at_nat,vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,X0),X1))),X2) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP3,X2),vAPP(list_P559422087at_nat,nat,size_s1990949619at_nat,X1)),vAPP(list_P559422087at_nat,nat,size_s1990949619at_nat,vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,X0),X1))) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP2,vAPP(list_P559422087at_nat,nat,size_s1990949619at_nat,X1)),X2),vAPP(list_P559422087at_nat,nat,size_s1990949619at_nat,vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,X0),X1))) ) )
| ~ spl155_100
| ~ spl155_149 ),
inference(trivial_inequality_removal,[],[f4226]) ).
thf(f4226,plain,
( ! [X2: nat,X0: product_prod_nat_nat,X1: list_P559422087at_nat] :
( ( $true != $true )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP5,vAPP(list_P559422087at_nat,nat,size_s1990949619at_nat,vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,X0),X1))),X2),vAPP(list_P559422087at_nat,nat,size_s1990949619at_nat,X1)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP4,vAPP(list_P559422087at_nat,nat,size_s1990949619at_nat,X1)),vAPP(list_P559422087at_nat,nat,size_s1990949619at_nat,vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,X0),X1))),X2) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP3,X2),vAPP(list_P559422087at_nat,nat,size_s1990949619at_nat,X1)),vAPP(list_P559422087at_nat,nat,size_s1990949619at_nat,vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,X0),X1))) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP2,vAPP(list_P559422087at_nat,nat,size_s1990949619at_nat,X1)),X2),vAPP(list_P559422087at_nat,nat,size_s1990949619at_nat,vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,X0),X1))) ) )
| ~ spl155_100
| ~ spl155_149 ),
inference(superposition,[],[f3437,f4213]) ).
thf(f12835,plain,
( spl155_548
| ~ spl155_126
| ~ spl155_149 ),
inference(avatar_split_clause,[],[f4291,f4212,f3768,f12833]) ).
thf(f12833,plain,
( spl155_548
<=> ! [X2: nat,X0: set_nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,X0),X1) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP5,vAPP(set_nat,nat,finite_card_nat,vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK14,X0),X1))),X2),X1) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP4,X1),vAPP(set_nat,nat,finite_card_nat,vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK14,X0),X1))),X2) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP3,X2),X1),vAPP(set_nat,nat,finite_card_nat,vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK14,X0),X1))) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP2,X1),X2),vAPP(set_nat,nat,finite_card_nat,vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK14,X0),X1))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_548])]) ).
thf(f4291,plain,
( ! [X2: nat,X0: set_nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,X0),X1) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP5,vAPP(set_nat,nat,finite_card_nat,vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK14,X0),X1))),X2),X1) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP4,X1),vAPP(set_nat,nat,finite_card_nat,vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK14,X0),X1))),X2) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP3,X2),X1),vAPP(set_nat,nat,finite_card_nat,vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK14,X0),X1))) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP2,X1),X2),vAPP(set_nat,nat,finite_card_nat,vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK14,X0),X1))) ) )
| ~ spl155_126
| ~ spl155_149 ),
inference(trivial_inequality_removal,[],[f4216]) ).
thf(f4216,plain,
( ! [X2: nat,X0: set_nat,X1: nat] :
( ( $true != $true )
| ( $true != vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,X0),X1) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP5,vAPP(set_nat,nat,finite_card_nat,vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK14,X0),X1))),X2),X1) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP4,X1),vAPP(set_nat,nat,finite_card_nat,vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK14,X0),X1))),X2) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP3,X2),X1),vAPP(set_nat,nat,finite_card_nat,vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK14,X0),X1))) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP2,X1),X2),vAPP(set_nat,nat,finite_card_nat,vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK14,X0),X1))) ) )
| ~ spl155_126
| ~ spl155_149 ),
inference(superposition,[],[f3769,f4213]) ).
thf(f12831,plain,
( spl155_547
| ~ spl155_127
| ~ spl155_149 ),
inference(avatar_split_clause,[],[f4290,f4212,f3772,f12829]) ).
thf(f12829,plain,
( spl155_547
<=> ! [X2: nat,X0: set_Pr1986765409at_nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(nat,$o),sP1,X0),X1) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP5,vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK17,X0),X1))),X2),X1) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP4,X1),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK17,X0),X1))),X2) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP3,X2),X1),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK17,X0),X1))) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP2,X1),X2),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK17,X0),X1))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_547])]) ).
thf(f4290,plain,
( ! [X2: nat,X0: set_Pr1986765409at_nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(nat,$o),sP1,X0),X1) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP5,vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK17,X0),X1))),X2),X1) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP4,X1),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK17,X0),X1))),X2) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP3,X2),X1),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK17,X0),X1))) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP2,X1),X2),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK17,X0),X1))) ) )
| ~ spl155_127
| ~ spl155_149 ),
inference(trivial_inequality_removal,[],[f4217]) ).
thf(f4217,plain,
( ! [X2: nat,X0: set_Pr1986765409at_nat,X1: nat] :
( ( $true != $true )
| ( $true != vAPP(nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(nat,$o),sP1,X0),X1) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP5,vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK17,X0),X1))),X2),X1) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP4,X1),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK17,X0),X1))),X2) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP3,X2),X1),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK17,X0),X1))) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP2,X1),X2),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK17,X0),X1))) ) )
| ~ spl155_127
| ~ spl155_149 ),
inference(superposition,[],[f3773,f4213]) ).
thf(f12827,plain,
( spl155_546
| ~ spl155_2
| ~ spl155_64 ),
inference(avatar_split_clause,[],[f3191,f3187,f2739,f12825]) ).
thf(f12825,plain,
( spl155_546
<=> ! [X0: nat > list_P559422087at_nat > nat > $o,X3: nat,X2: list_P559422087at_nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),X0,X1),X2),X3) )
| ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),X0,vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),nat,sK93,X0)),nil_Pr1308055047at_nat),vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),nat,sK94,X0)) )
| ( $false = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),X0,vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),nat,sK88,X0)),vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),nat,sK89,X0)),vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),nat,sK90,X0))),vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),list_P559422087at_nat,sK91,X0))),vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),nat,sK92,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_546])]) ).
thf(f3187,plain,
( spl155_64
<=> ! [X0: nat > list_P559422087at_nat > nat > $o,X3: nat,X2: list_P559422087at_nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),X0,X1),X2),X3) )
| ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),X0,vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),nat,sK88,X0)),vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),nat,sK89,X0)),vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),nat,sK90,X0))),vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),list_P559422087at_nat,sK91,X0))),vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),nat,sK92,X0)) )
| ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),X0,vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),nat,sK93,X0)),nil_Pr1308055047at_nat),vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),nat,sK94,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_64])]) ).
thf(f3191,plain,
( ! [X2: list_P559422087at_nat,X3: nat,X0: nat > list_P559422087at_nat > nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),X0,X1),X2),X3) )
| ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),X0,vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),nat,sK93,X0)),nil_Pr1308055047at_nat),vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),nat,sK94,X0)) )
| ( $false = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),X0,vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),nat,sK88,X0)),vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),nat,sK89,X0)),vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),nat,sK90,X0))),vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),list_P559422087at_nat,sK91,X0))),vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),nat,sK92,X0)) ) )
| ~ spl155_2
| ~ spl155_64 ),
inference(trivial_inequality_removal,[],[f3190]) ).
thf(f3190,plain,
( ! [X2: list_P559422087at_nat,X3: nat,X0: nat > list_P559422087at_nat > nat > $o,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),X0,X1),X2),X3) )
| ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),X0,vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),nat,sK93,X0)),nil_Pr1308055047at_nat),vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),nat,sK94,X0)) )
| ( $false = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),X0,vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),nat,sK88,X0)),vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),nat,sK89,X0)),vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),nat,sK90,X0))),vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),list_P559422087at_nat,sK91,X0))),vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),nat,sK92,X0)) ) )
| ~ spl155_2
| ~ spl155_64 ),
inference(superposition,[],[f3188,f2740]) ).
thf(f3188,plain,
( ! [X2: list_P559422087at_nat,X3: nat,X0: nat > list_P559422087at_nat > nat > $o,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),X0,vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),nat,sK88,X0)),vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),nat,sK89,X0)),vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),nat,sK90,X0))),vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),list_P559422087at_nat,sK91,X0))),vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),nat,sK92,X0)) )
| ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),X0,X1),X2),X3) )
| ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),X0,vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),nat,sK93,X0)),nil_Pr1308055047at_nat),vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),nat,sK94,X0)) ) )
| ~ spl155_64 ),
inference(avatar_component_clause,[],[f3187]) ).
thf(f12821,plain,
( spl155_545
| ~ spl155_370
| ~ spl155_466 ),
inference(avatar_split_clause,[],[f10140,f10040,f7694,f12819]) ).
thf(f12819,plain,
( spl155_545
<=> ! [X0: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p))) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,X0),edges)),edges) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_545])]) ).
thf(f7694,plain,
( spl155_370
<=> ! [X0: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p))) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_370])]) ).
thf(f10040,plain,
( spl155_466
<=> ! [X0: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),X0) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,X0),edges)),edges) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_466])]) ).
thf(f10140,plain,
( ! [X0: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p))) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,X0),edges)),edges) ) )
| ~ spl155_370
| ~ spl155_466 ),
inference(trivial_inequality_removal,[],[f10103]) ).
thf(f10103,plain,
( ! [X0: set_Pr1986765409at_nat] :
( ( $true != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p))) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,X0),edges)),edges) ) )
| ~ spl155_370
| ~ spl155_466 ),
inference(superposition,[],[f7695,f10041]) ).
thf(f10041,plain,
( ! [X0: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),X0) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,X0),edges)),edges) ) )
| ~ spl155_466 ),
inference(avatar_component_clause,[],[f10040]) ).
thf(f7695,plain,
( ! [X0: set_Pr1986765409at_nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),X0) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p))) ) )
| ~ spl155_370 ),
inference(avatar_component_clause,[],[f7694]) ).
thf(f12817,plain,
( spl155_544
| ~ spl155_2
| ~ spl155_124 ),
inference(avatar_split_clause,[],[f3760,f3711,f2739,f12815]) ).
thf(f12815,plain,
( spl155_544
<=> ! [X2: nat,X0: nat,X1: list_P559422087at_nat] :
( ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),vAPP($o,sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat))),sK85,$true),X2),X1),X0)),vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),vAPP($o,sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat))),sK86,$true),X2),X1),X0))),vAPP(nat,list_P559422087at_nat,vAPP(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat)),vAPP($o,sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat))),sK87,$true),X2),X1),X0)) = X1 )
| ( nil_Pr1308055047at_nat = X1 )
| ( $false = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_544])]) ).
thf(f3711,plain,
( spl155_124
<=> ! [X2: nat,X0: nat,X1: list_P559422087at_nat] :
( ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),vAPP($o,sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat))),sK85,vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2)),X2),X1),X0)),vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),vAPP($o,sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat))),sK86,vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2)),X2),X1),X0))),vAPP(nat,list_P559422087at_nat,vAPP(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat)),vAPP($o,sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat))),sK87,vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2)),X2),X1),X0)) = X1 )
| ( nil_Pr1308055047at_nat = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_124])]) ).
thf(f3760,plain,
( ! [X2: nat,X0: nat,X1: list_P559422087at_nat] :
( ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),vAPP($o,sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat))),sK85,$true),X2),X1),X0)),vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),vAPP($o,sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat))),sK86,$true),X2),X1),X0))),vAPP(nat,list_P559422087at_nat,vAPP(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat)),vAPP($o,sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat))),sK87,$true),X2),X1),X0)) = X1 )
| ( nil_Pr1308055047at_nat = X1 )
| ( $false = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2) ) )
| ~ spl155_2
| ~ spl155_124 ),
inference(superposition,[],[f3712,f2740]) ).
thf(f3712,plain,
( ! [X2: nat,X0: nat,X1: list_P559422087at_nat] :
( ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),vAPP($o,sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat))),sK85,vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2)),X2),X1),X0)),vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),vAPP($o,sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat))),sK86,vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2)),X2),X1),X0))),vAPP(nat,list_P559422087at_nat,vAPP(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat)),vAPP($o,sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat))),sK87,vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2)),X2),X1),X0)) = X1 )
| ( nil_Pr1308055047at_nat = X1 ) )
| ~ spl155_124 ),
inference(avatar_component_clause,[],[f3711]) ).
thf(f12806,plain,
( spl155_542
| spl155_543
| ~ spl155_19
| ~ spl155_24 ),
inference(avatar_split_clause,[],[f2925,f2914,f2882,f12804,f12800]) ).
thf(f12800,plain,
( spl155_542
<=> ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isShortestPath_a,c),s),p),vAPP(sTfun(nat,$o),nat,sK60,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isShortestPath_a,c),s),p))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_542])]) ).
thf(f12804,plain,
( spl155_543
<=> ! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isShortestPath_a,c),s),p),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK61,X0),vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isShortestPath_a,c),s),p))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_543])]) ).
thf(f2882,plain,
( spl155_19
<=> ( vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isShortestPath_a,c),s),p),t) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_19])]) ).
thf(f2914,plain,
( spl155_24
<=> ! [X2: nat,X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK60,X0)) )
| ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK61,X2),X0)) )
| ( $true != vAPP(nat,$o,X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_24])]) ).
thf(f2925,plain,
( ! [X0: nat] :
( ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isShortestPath_a,c),s),p),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK61,X0),vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isShortestPath_a,c),s),p))) )
| ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isShortestPath_a,c),s),p),vAPP(sTfun(nat,$o),nat,sK60,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isShortestPath_a,c),s),p))) ) )
| ~ spl155_19
| ~ spl155_24 ),
inference(trivial_inequality_removal,[],[f2922]) ).
thf(f2922,plain,
( ! [X0: nat] :
( ( $true != $true )
| ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isShortestPath_a,c),s),p),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK61,X0),vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isShortestPath_a,c),s),p))) )
| ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isShortestPath_a,c),s),p),vAPP(sTfun(nat,$o),nat,sK60,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isShortestPath_a,c),s),p))) ) )
| ~ spl155_19
| ~ spl155_24 ),
inference(superposition,[],[f2915,f2884]) ).
thf(f2884,plain,
( ( vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isShortestPath_a,c),s),p),t) = $true )
| ~ spl155_19 ),
inference(avatar_component_clause,[],[f2882]) ).
thf(f2915,plain,
( ! [X2: nat,X0: nat > $o,X1: nat] :
( ( $true != vAPP(nat,$o,X0,X1) )
| ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK61,X2),X0)) )
| ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK60,X0)) ) )
| ~ spl155_24 ),
inference(avatar_component_clause,[],[f2914]) ).
thf(f12774,plain,
( spl155_541
| ~ spl155_119
| ~ spl155_150 ),
inference(avatar_split_clause,[],[f4304,f4294,f3632,f12772]) ).
thf(f12772,plain,
( spl155_541
<=> ! [X2: product_prod_nat_nat > a,X4: nat,X0: list_P559422087at_nat,X3: nat,X1: product_prod_nat_nat > a] :
( ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,X1),X3),X0),X4) )
| ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,X2),X3),X0),X4) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X2)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X0)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X1)))),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X0)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X1))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_541])]) ).
thf(f4294,plain,
( spl155_150
<=> ! [X4: nat,X0: list_P559422087at_nat,X3: nat,X2: product_prod_nat_nat > a,X1: product_prod_nat_nat > a] :
( ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,X2),X3),X0),X4) )
| ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,X1),X3),X0),X4) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X0)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X1))),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_150])]) ).
thf(f4304,plain,
( ! [X2: product_prod_nat_nat > a,X3: nat,X0: list_P559422087at_nat,X1: product_prod_nat_nat > a,X4: nat] :
( ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,X1),X3),X0),X4) )
| ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,X2),X3),X0),X4) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X2)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X0)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X1)))),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X0)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X1))) ) )
| ~ spl155_119
| ~ spl155_150 ),
inference(trivial_inequality_removal,[],[f4301]) ).
thf(f4301,plain,
( ! [X2: product_prod_nat_nat > a,X3: nat,X0: list_P559422087at_nat,X1: product_prod_nat_nat > a,X4: nat] :
( ( $true != $true )
| ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,X1),X3),X0),X4) )
| ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,X2),X3),X0),X4) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X2)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X0)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X1)))),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X0)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X1))) ) )
| ~ spl155_119
| ~ spl155_150 ),
inference(superposition,[],[f4295,f3633]) ).
thf(f4295,plain,
( ! [X2: product_prod_nat_nat > a,X3: nat,X0: list_P559422087at_nat,X1: product_prod_nat_nat > a,X4: nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X0)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X1))),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X2)) )
| ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,X1),X3),X0),X4) )
| ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,X2),X3),X0),X4) ) )
| ~ spl155_150 ),
inference(avatar_component_clause,[],[f4294]) ).
thf(f12769,plain,
spl155_540,
inference(avatar_split_clause,[],[f2557,f12767]) ).
thf(f12767,plain,
( spl155_540
<=> ! [X4: nat,X0: nat,X3: list_P559422087at_nat,X2: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X1),X2)),X3)),X4) )
| ( $false = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X2),X3),X4) )
| ( $false = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X1),X2)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) )
| ( X0 != X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_540])]) ).
thf(f2557,plain,
! [X2: nat,X3: list_P559422087at_nat,X0: nat,X1: nat,X4: nat] :
( ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X1),X2)),X3)),X4) )
| ( $false = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X2),X3),X4) )
| ( $false = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X1),X2)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) )
| ( X0 != X1 ) ),
inference(equality_proxy_clausification,[],[f2556]) ).
thf(f2556,plain,
! [X2: nat,X3: list_P559422087at_nat,X0: nat,X1: nat,X4: nat] :
( ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X1),X2)),X3)),X4) )
| ( $false = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X2),X3),X4) )
| ( $false = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X1),X2)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) ) ),
inference(binary_proxy_clausification,[],[f2555]) ).
thf(f2555,plain,
! [X2: nat,X3: list_P559422087at_nat,X0: nat,X1: nat,X4: nat] :
( ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X1),X2)),X3)),X4) )
| ( $false = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X2),X3),X4) )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1)),vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X1),X2)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c))) ) ),
inference(binary_proxy_clausification,[],[f2548]) ).
thf(f2548,plain,
! [X2: nat,X3: list_P559422087at_nat,X0: nat,X1: nat,X4: nat] :
( ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X1),X2)),X3)),X4) )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1)),vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X1),X2)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)))),vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X2),X3),X4)) ) ),
inference(binary_proxy_clausification,[],[f2079]) ).
thf(f2079,plain,
! [X2: nat,X3: list_P559422087at_nat,X0: nat,X1: nat,X4: nat] : ( vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X1),X2)),X3)),X4) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1)),vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X1),X2)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)))),vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X2),X3),X4)) ),
inference(cnf_transformation,[],[f999]) ).
thf(f999,plain,
! [X0: nat,X1: nat,X2: nat,X3: list_P559422087at_nat,X4: nat] : ( vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X1),X2)),X3)),X4) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1)),vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X1),X2)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)))),vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X2),X3),X4)) ),
inference(fool_elimination,[],[f998]) ).
thf(f998,plain,
! [X0: nat,X1: nat,X2: nat,X3: list_P559422087at_nat,X4: nat] :
( ( vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X1),X2)),X3)),X4) = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X2),X3),X4) )
& vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X1),X2)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c))
& ( X0 = X1 ) ),
inference(rectify,[],[f340]) ).
thf(f340,axiom,
! [X1: nat,X5: nat,X21: nat,X6: list_P559422087at_nat,X7: nat] :
( ( vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X1),vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X5),X21)),X6)),X7) = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X21),X6),X7) )
& vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X5),X21)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c))
& ( X1 = X5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_339_isPath_Osimps_I2_J) ).
thf(f12452,plain,
( spl155_539
| ~ spl155_105
| ~ spl155_149 ),
inference(avatar_split_clause,[],[f4284,f4212,f3488,f12450]) ).
thf(f12450,plain,
( spl155_539
<=> ! [X2: nat,X0: nat,X1: set_Pr1986765409at_nat] :
( ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK28,X1),X0)) = X0 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP5,X0),X2),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP4,vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)),X0),X2) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP3,X2),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)),X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP2,vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)),X2),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_539])]) ).
thf(f4284,plain,
( ! [X2: nat,X0: nat,X1: set_Pr1986765409at_nat] :
( ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK28,X1),X0)) = X0 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP5,X0),X2),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP4,vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)),X0),X2) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP3,X2),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)),X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP2,vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)),X2),X0) ) )
| ~ spl155_105
| ~ spl155_149 ),
inference(trivial_inequality_removal,[],[f4223]) ).
thf(f4223,plain,
( ! [X2: nat,X0: nat,X1: set_Pr1986765409at_nat] :
( ( $true != $true )
| ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK28,X1),X0)) = X0 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP5,X0),X2),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP4,vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)),X0),X2) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP3,X2),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)),X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP2,vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)),X2),X0) ) )
| ~ spl155_105
| ~ spl155_149 ),
inference(superposition,[],[f3489,f4213]) ).
thf(f12448,plain,
( spl155_538
| ~ spl155_104
| ~ spl155_149 ),
inference(avatar_split_clause,[],[f4283,f4212,f3484,f12446]) ).
thf(f12446,plain,
( spl155_538
<=> ! [X2: nat,X0: nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK28,X1),X0)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP5,X0),X2),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP4,vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)),X0),X2) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP3,X2),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)),X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP2,vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)),X2),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_538])]) ).
thf(f4283,plain,
( ! [X2: nat,X0: nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK28,X1),X0)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP5,X0),X2),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP4,vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)),X0),X2) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP3,X2),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)),X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP2,vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)),X2),X0) ) )
| ~ spl155_104
| ~ spl155_149 ),
inference(trivial_inequality_removal,[],[f4224]) ).
thf(f4224,plain,
( ! [X2: nat,X0: nat,X1: set_Pr1986765409at_nat] :
( ( $true != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK28,X1),X0)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP5,X0),X2),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP4,vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)),X0),X2) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP3,X2),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)),X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP2,vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)),X2),X0) ) )
| ~ spl155_104
| ~ spl155_149 ),
inference(superposition,[],[f3485,f4213]) ).
thf(f12444,plain,
( spl155_537
| ~ spl155_103
| ~ spl155_149 ),
inference(avatar_split_clause,[],[f4282,f4212,f3480,f12442]) ).
thf(f12442,plain,
( spl155_537
<=> ! [X2: nat,X0: nat,X1: set_nat] :
( ( vAPP(set_nat,nat,finite_card_nat,vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK27,X1),X0)) = X0 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP5,X0),X2),vAPP(set_nat,nat,finite_card_nat,X1)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP4,vAPP(set_nat,nat,finite_card_nat,X1)),X0),X2) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP3,X2),vAPP(set_nat,nat,finite_card_nat,X1)),X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP2,vAPP(set_nat,nat,finite_card_nat,X1)),X2),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_537])]) ).
thf(f4282,plain,
( ! [X2: nat,X0: nat,X1: set_nat] :
( ( vAPP(set_nat,nat,finite_card_nat,vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK27,X1),X0)) = X0 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP5,X0),X2),vAPP(set_nat,nat,finite_card_nat,X1)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP4,vAPP(set_nat,nat,finite_card_nat,X1)),X0),X2) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP3,X2),vAPP(set_nat,nat,finite_card_nat,X1)),X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP2,vAPP(set_nat,nat,finite_card_nat,X1)),X2),X0) ) )
| ~ spl155_103
| ~ spl155_149 ),
inference(trivial_inequality_removal,[],[f4225]) ).
thf(f4225,plain,
( ! [X2: nat,X0: nat,X1: set_nat] :
( ( $true != $true )
| ( vAPP(set_nat,nat,finite_card_nat,vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK27,X1),X0)) = X0 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP5,X0),X2),vAPP(set_nat,nat,finite_card_nat,X1)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP4,vAPP(set_nat,nat,finite_card_nat,X1)),X0),X2) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP3,X2),vAPP(set_nat,nat,finite_card_nat,X1)),X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP2,vAPP(set_nat,nat,finite_card_nat,X1)),X2),X0) ) )
| ~ spl155_103
| ~ spl155_149 ),
inference(superposition,[],[f3481,f4213]) ).
thf(f12330,plain,
( spl155_536
| ~ spl155_2
| ~ spl155_62 ),
inference(avatar_split_clause,[],[f3181,f3177,f2739,f12328]) ).
thf(f12328,plain,
( spl155_536
<=> ! [X0: nat > list_P559422087at_nat > nat > $o,X3: nat,X2: list_P559422087at_nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),X0,vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),nat,sK90,X0)),vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),list_P559422087at_nat,sK91,X0)),vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),nat,sK92,X0)) )
| ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),X0,X1),X2),X3) )
| ( $false = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),X0,vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),nat,sK93,X0)),nil_Pr1308055047at_nat),vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),nat,sK94,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_536])]) ).
thf(f3177,plain,
( spl155_62
<=> ! [X0: nat > list_P559422087at_nat > nat > $o,X3: nat,X2: list_P559422087at_nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),X0,X1),X2),X3) )
| ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),X0,vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),nat,sK90,X0)),vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),list_P559422087at_nat,sK91,X0)),vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),nat,sK92,X0)) )
| ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),X0,vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),nat,sK93,X0)),nil_Pr1308055047at_nat),vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),nat,sK94,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_62])]) ).
thf(f3181,plain,
( ! [X2: list_P559422087at_nat,X3: nat,X0: nat > list_P559422087at_nat > nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),X0,vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),nat,sK90,X0)),vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),list_P559422087at_nat,sK91,X0)),vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),nat,sK92,X0)) )
| ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),X0,X1),X2),X3) )
| ( $false = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),X0,vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),nat,sK93,X0)),nil_Pr1308055047at_nat),vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),nat,sK94,X0)) ) )
| ~ spl155_2
| ~ spl155_62 ),
inference(trivial_inequality_removal,[],[f3180]) ).
thf(f3180,plain,
( ! [X2: list_P559422087at_nat,X3: nat,X0: nat > list_P559422087at_nat > nat > $o,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),X0,vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),nat,sK90,X0)),vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),list_P559422087at_nat,sK91,X0)),vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),nat,sK92,X0)) )
| ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),X0,X1),X2),X3) )
| ( $false = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),X0,vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),nat,sK93,X0)),nil_Pr1308055047at_nat),vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),nat,sK94,X0)) ) )
| ~ spl155_2
| ~ spl155_62 ),
inference(superposition,[],[f3178,f2740]) ).
thf(f3178,plain,
( ! [X2: list_P559422087at_nat,X3: nat,X0: nat > list_P559422087at_nat > nat > $o,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),X0,vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),nat,sK93,X0)),nil_Pr1308055047at_nat),vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),nat,sK94,X0)) )
| ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),X0,vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),nat,sK90,X0)),vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),list_P559422087at_nat,sK91,X0)),vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),nat,sK92,X0)) )
| ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),X0,X1),X2),X3) ) )
| ~ spl155_62 ),
inference(avatar_component_clause,[],[f3177]) ).
thf(f12324,plain,
( spl155_535
| ~ spl155_91
| ~ spl155_144 ),
inference(avatar_split_clause,[],[f4052,f4023,f3382,f12322]) ).
thf(f12322,plain,
( spl155_535
<=> ! [X2: set_se1612935105at_nat,X0: nat,X1: set_Pr1986765409at_nat] :
( ( vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK20,X1),X2) = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sK11,X0),vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK20,X1),X2)) )
| ( $true != vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sK11,X0),vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK20,X1),X2))),X2) )
| ( $true != vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X1),X2) )
| ( vAPP(set_se1612935105at_nat,$o,finite1457549322at_nat,X2) != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK20,X1),X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_535])]) ).
thf(f4023,plain,
( spl155_144
<=> ! [X0: set_se1612935105at_nat,X1: set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat] :
( ( vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK20,X1),X0) = X3 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X3),vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK20,X1),X0)) )
| ( $true != vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X3),X0) )
| ( $true != vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X1),X0) )
| ( $true != vAPP(set_se1612935105at_nat,$o,finite1457549322at_nat,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_144])]) ).
thf(f4052,plain,
( ! [X2: set_se1612935105at_nat,X0: nat,X1: set_Pr1986765409at_nat] :
( ( vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK20,X1),X2) = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sK11,X0),vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK20,X1),X2)) )
| ( $true != vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sK11,X0),vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK20,X1),X2))),X2) )
| ( $true != vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X1),X2) )
| ( vAPP(set_se1612935105at_nat,$o,finite1457549322at_nat,X2) != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK20,X1),X2)) ) )
| ~ spl155_91
| ~ spl155_144 ),
inference(trivial_inequality_removal,[],[f4047]) ).
thf(f4047,plain,
( ! [X2: set_se1612935105at_nat,X0: nat,X1: set_Pr1986765409at_nat] :
( ( $true != $true )
| ( vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK20,X1),X2) = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sK11,X0),vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK20,X1),X2)) )
| ( $true != vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sK11,X0),vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK20,X1),X2))),X2) )
| ( $true != vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X1),X2) )
| ( vAPP(set_se1612935105at_nat,$o,finite1457549322at_nat,X2) != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK20,X1),X2)) ) )
| ~ spl155_91
| ~ spl155_144 ),
inference(superposition,[],[f4024,f3383]) ).
thf(f4024,plain,
( ! [X3: set_Pr1986765409at_nat,X0: set_se1612935105at_nat,X1: set_Pr1986765409at_nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X3),vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK20,X1),X0)) )
| ( vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK20,X1),X0) = X3 )
| ( $true != vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X3),X0) )
| ( $true != vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X1),X0) )
| ( $true != vAPP(set_se1612935105at_nat,$o,finite1457549322at_nat,X0) ) )
| ~ spl155_144 ),
inference(avatar_component_clause,[],[f4023]) ).
thf(f12249,plain,
( spl155_534
| ~ spl155_2
| ~ spl155_58 ),
inference(avatar_split_clause,[],[f3167,f3152,f2739,f12247]) ).
thf(f12247,plain,
( spl155_534
<=> ! [X2: list_P559422087at_nat,X3: nat,X4: nat,X0: product_prod_nat_nat > a,X5: nat,X1: nat] :
( ( X1 = X4 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X4),X5)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X2)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(list_P559422087at_nat,nat,vAPP(nat,sTfun(list_P559422087at_nat,nat),sK154,X4),X2)),X4)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X2)) )
| ( $false = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,X0),X1),X2),X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_534])]) ).
thf(f3152,plain,
( spl155_58
<=> ! [X3: nat,X4: nat,X0: product_prod_nat_nat > a,X5: nat,X2: list_P559422087at_nat,X1: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(list_P559422087at_nat,nat,vAPP(nat,sTfun(list_P559422087at_nat,nat),sK154,X4),X2)),X4)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X2)) )
| ( X1 = X4 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X4),X5)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X2)) )
| ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,X0),X1),X2),X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_58])]) ).
thf(f3167,plain,
( ! [X2: list_P559422087at_nat,X3: nat,X0: product_prod_nat_nat > a,X1: nat,X4: nat,X5: nat] :
( ( X1 = X4 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X4),X5)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X2)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(list_P559422087at_nat,nat,vAPP(nat,sTfun(list_P559422087at_nat,nat),sK154,X4),X2)),X4)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X2)) )
| ( $false = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,X0),X1),X2),X3) ) )
| ~ spl155_2
| ~ spl155_58 ),
inference(trivial_inequality_removal,[],[f3166]) ).
thf(f3166,plain,
( ! [X2: list_P559422087at_nat,X3: nat,X0: product_prod_nat_nat > a,X1: nat,X4: nat,X5: nat] :
( ( $true != $true )
| ( X1 = X4 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X4),X5)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X2)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(list_P559422087at_nat,nat,vAPP(nat,sTfun(list_P559422087at_nat,nat),sK154,X4),X2)),X4)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X2)) )
| ( $false = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,X0),X1),X2),X3) ) )
| ~ spl155_2
| ~ spl155_58 ),
inference(superposition,[],[f3153,f2740]) ).
thf(f3153,plain,
( ! [X2: list_P559422087at_nat,X3: nat,X0: product_prod_nat_nat > a,X1: nat,X4: nat,X5: nat] :
( ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,X0),X1),X2),X3) )
| ( X1 = X4 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X4),X5)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X2)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(list_P559422087at_nat,nat,vAPP(nat,sTfun(list_P559422087at_nat,nat),sK154,X4),X2)),X4)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X2)) ) )
| ~ spl155_58 ),
inference(avatar_component_clause,[],[f3152]) ).
thf(f12245,plain,
( spl155_533
| ~ spl155_2
| ~ spl155_57 ),
inference(avatar_split_clause,[],[f3165,f3148,f2739,f12243]) ).
thf(f12243,plain,
( spl155_533
<=> ! [X3: nat,X4: nat,X0: product_prod_nat_nat > a,X5: nat,X2: list_P559422087at_nat,X1: nat] :
( ( X3 = X4 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X5),X4)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X2)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X4),vAPP(list_P559422087at_nat,nat,vAPP(nat,sTfun(list_P559422087at_nat,nat),sK153,X4),X2))),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X2)) )
| ( $false = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,X0),X1),X2),X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_533])]) ).
thf(f3148,plain,
( spl155_57
<=> ! [X3: nat,X4: nat,X0: product_prod_nat_nat > a,X5: nat,X2: list_P559422087at_nat,X1: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X5),vAPP(list_P559422087at_nat,nat,vAPP(nat,sTfun(list_P559422087at_nat,nat),sK153,X5),X2))),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X2)) )
| ( X3 = X5 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X4),X5)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X2)) )
| ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,X0),X1),X2),X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_57])]) ).
thf(f3165,plain,
( ! [X2: list_P559422087at_nat,X3: nat,X0: product_prod_nat_nat > a,X1: nat,X4: nat,X5: nat] :
( ( X3 = X4 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X5),X4)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X2)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X4),vAPP(list_P559422087at_nat,nat,vAPP(nat,sTfun(list_P559422087at_nat,nat),sK153,X4),X2))),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X2)) )
| ( $false = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,X0),X1),X2),X3) ) )
| ~ spl155_2
| ~ spl155_57 ),
inference(trivial_inequality_removal,[],[f3164]) ).
thf(f3164,plain,
( ! [X2: list_P559422087at_nat,X3: nat,X0: product_prod_nat_nat > a,X1: nat,X4: nat,X5: nat] :
( ( $true != $true )
| ( X3 = X4 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X5),X4)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X2)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X4),vAPP(list_P559422087at_nat,nat,vAPP(nat,sTfun(list_P559422087at_nat,nat),sK153,X4),X2))),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X2)) )
| ( $false = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,X0),X1),X2),X3) ) )
| ~ spl155_2
| ~ spl155_57 ),
inference(superposition,[],[f3149,f2740]) ).
thf(f3149,plain,
( ! [X2: list_P559422087at_nat,X3: nat,X0: product_prod_nat_nat > a,X1: nat,X4: nat,X5: nat] :
( ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,X0),X1),X2),X3) )
| ( X3 = X5 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X4),X5)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X2)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X5),vAPP(list_P559422087at_nat,nat,vAPP(nat,sTfun(list_P559422087at_nat,nat),sK153,X5),X2))),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X2)) ) )
| ~ spl155_57 ),
inference(avatar_component_clause,[],[f3148]) ).
thf(f12241,plain,
( spl155_532
| ~ spl155_2
| ~ spl155_56 ),
inference(avatar_split_clause,[],[f3163,f3144,f2739,f12239]) ).
thf(f12239,plain,
( spl155_532
<=> ! [X2: nat,X4: nat,X0: nat,X3: nat,X1: list_P559422087at_nat] :
( ( X0 = X3 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X3),X4)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X1)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(list_P559422087at_nat,nat,vAPP(nat,sTfun(list_P559422087at_nat,nat),sK152,X3),X1)),X3)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X1)) )
| ( $false = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_532])]) ).
thf(f3144,plain,
( spl155_56
<=> ! [X2: nat,X4: nat,X0: nat,X3: nat,X1: list_P559422087at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(list_P559422087at_nat,nat,vAPP(nat,sTfun(list_P559422087at_nat,nat),sK152,X3),X1)),X3)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X1)) )
| ( X0 = X3 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X3),X4)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X1)) )
| ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_56])]) ).
thf(f3163,plain,
( ! [X2: nat,X3: nat,X0: nat,X1: list_P559422087at_nat,X4: nat] :
( ( X0 = X3 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X3),X4)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X1)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(list_P559422087at_nat,nat,vAPP(nat,sTfun(list_P559422087at_nat,nat),sK152,X3),X1)),X3)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X1)) )
| ( $false = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2) ) )
| ~ spl155_2
| ~ spl155_56 ),
inference(trivial_inequality_removal,[],[f3162]) ).
thf(f3162,plain,
( ! [X2: nat,X3: nat,X0: nat,X1: list_P559422087at_nat,X4: nat] :
( ( $true != $true )
| ( X0 = X3 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X3),X4)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X1)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(list_P559422087at_nat,nat,vAPP(nat,sTfun(list_P559422087at_nat,nat),sK152,X3),X1)),X3)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X1)) )
| ( $false = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2) ) )
| ~ spl155_2
| ~ spl155_56 ),
inference(superposition,[],[f3145,f2740]) ).
thf(f3145,plain,
( ! [X2: nat,X3: nat,X0: nat,X1: list_P559422087at_nat,X4: nat] :
( ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2) )
| ( X0 = X3 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X3),X4)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X1)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(list_P559422087at_nat,nat,vAPP(nat,sTfun(list_P559422087at_nat,nat),sK152,X3),X1)),X3)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X1)) ) )
| ~ spl155_56 ),
inference(avatar_component_clause,[],[f3144]) ).
thf(f12237,plain,
( spl155_531
| ~ spl155_2
| ~ spl155_55 ),
inference(avatar_split_clause,[],[f3161,f3140,f2739,f12235]) ).
thf(f12235,plain,
( spl155_531
<=> ! [X4: nat,X0: nat,X3: nat,X2: nat,X1: list_P559422087at_nat] :
( ( X2 = X3 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X4),X3)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X1)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X3),vAPP(list_P559422087at_nat,nat,vAPP(nat,sTfun(list_P559422087at_nat,nat),sK151,X3),X1))),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X1)) )
| ( $false = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_531])]) ).
thf(f3140,plain,
( spl155_55
<=> ! [X2: nat,X4: nat,X0: nat,X3: nat,X1: list_P559422087at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X4),vAPP(list_P559422087at_nat,nat,vAPP(nat,sTfun(list_P559422087at_nat,nat),sK151,X4),X1))),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X1)) )
| ( X2 = X4 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X3),X4)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X1)) )
| ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_55])]) ).
thf(f3161,plain,
( ! [X2: nat,X3: nat,X0: nat,X1: list_P559422087at_nat,X4: nat] :
( ( X2 = X3 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X4),X3)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X1)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X3),vAPP(list_P559422087at_nat,nat,vAPP(nat,sTfun(list_P559422087at_nat,nat),sK151,X3),X1))),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X1)) )
| ( $false = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2) ) )
| ~ spl155_2
| ~ spl155_55 ),
inference(trivial_inequality_removal,[],[f3160]) ).
thf(f3160,plain,
( ! [X2: nat,X3: nat,X0: nat,X1: list_P559422087at_nat,X4: nat] :
( ( $true != $true )
| ( X2 = X3 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X4),X3)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X1)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X3),vAPP(list_P559422087at_nat,nat,vAPP(nat,sTfun(list_P559422087at_nat,nat),sK151,X3),X1))),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X1)) )
| ( $false = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2) ) )
| ~ spl155_2
| ~ spl155_55 ),
inference(superposition,[],[f3141,f2740]) ).
thf(f3141,plain,
( ! [X2: nat,X3: nat,X0: nat,X1: list_P559422087at_nat,X4: nat] :
( ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2) )
| ( X2 = X4 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X3),X4)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X1)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X4),vAPP(list_P559422087at_nat,nat,vAPP(nat,sTfun(list_P559422087at_nat,nat),sK151,X4),X1))),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X1)) ) )
| ~ spl155_55 ),
inference(avatar_component_clause,[],[f3140]) ).
thf(f12230,plain,
( spl155_530
| ~ spl155_2
| ~ spl155_54 ),
inference(avatar_split_clause,[],[f3138,f3134,f2739,f12228]) ).
thf(f12228,plain,
( spl155_530
<=> ! [X2: nat,X0: list_P559422087at_nat,X1: nat] :
( ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,nat)),sK64,X0),X1),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,nat)),sK65,X0),X1),X2))),vAPP(nat,list_P559422087at_nat,vAPP(nat,sTfun(nat,list_P559422087at_nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,list_P559422087at_nat)),sK66,X0),X1),X2)) = X0 )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,$o)),sP7,X0),X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_530])]) ).
thf(f3134,plain,
( spl155_54
<=> ! [X2: list_P559422087at_nat,X0: nat,X1: nat] :
( ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,nat)),sK64,X2),X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,nat)),sK65,X2),X1),X0))),vAPP(nat,list_P559422087at_nat,vAPP(nat,sTfun(nat,list_P559422087at_nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,list_P559422087at_nat)),sK66,X2),X1),X0)) = X2 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,$o)),sP7,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_54])]) ).
thf(f3138,plain,
( ! [X2: nat,X0: list_P559422087at_nat,X1: nat] :
( ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,nat)),sK64,X0),X1),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,nat)),sK65,X0),X1),X2))),vAPP(nat,list_P559422087at_nat,vAPP(nat,sTfun(nat,list_P559422087at_nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,list_P559422087at_nat)),sK66,X0),X1),X2)) = X0 )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,$o)),sP7,X0),X1),X2) ) )
| ~ spl155_2
| ~ spl155_54 ),
inference(trivial_inequality_removal,[],[f3137]) ).
thf(f3137,plain,
( ! [X2: nat,X0: list_P559422087at_nat,X1: nat] :
( ( $true != $true )
| ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,nat)),sK64,X0),X1),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,nat)),sK65,X0),X1),X2))),vAPP(nat,list_P559422087at_nat,vAPP(nat,sTfun(nat,list_P559422087at_nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,list_P559422087at_nat)),sK66,X0),X1),X2)) = X0 )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,$o)),sP7,X0),X1),X2) ) )
| ~ spl155_2
| ~ spl155_54 ),
inference(superposition,[],[f3135,f2740]) ).
thf(f3135,plain,
( ! [X2: list_P559422087at_nat,X0: nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,$o)),sP7,X2),X1),X0) )
| ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,nat)),sK64,X2),X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,nat)),sK65,X2),X1),X0))),vAPP(nat,list_P559422087at_nat,vAPP(nat,sTfun(nat,list_P559422087at_nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,list_P559422087at_nat)),sK66,X2),X1),X0)) = X2 ) )
| ~ spl155_54 ),
inference(avatar_component_clause,[],[f3134]) ).
thf(f12074,plain,
( spl155_529
| ~ spl155_87
| ~ spl155_149 ),
inference(avatar_split_clause,[],[f4289,f4212,f3293,f12072]) ).
thf(f12072,plain,
( spl155_529
<=> ! [X2: nat,X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X1),X0) = X0 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP5,X0),X2),X1) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP4,X1),X0),X2) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP3,X2),X1),X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP2,X1),X2),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_529])]) ).
thf(f4289,plain,
( ! [X2: nat,X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X1),X0) = X0 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP5,X0),X2),X1) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP4,X1),X0),X2) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP3,X2),X1),X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP2,X1),X2),X0) ) )
| ~ spl155_87
| ~ spl155_149 ),
inference(trivial_inequality_removal,[],[f4218]) ).
thf(f4218,plain,
( ! [X2: nat,X0: nat,X1: nat] :
( ( $true != $true )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X1),X0) = X0 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP5,X0),X2),X1) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP4,X1),X0),X2) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP3,X2),X1),X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP2,X1),X2),X0) ) )
| ~ spl155_87
| ~ spl155_149 ),
inference(superposition,[],[f3294,f4213]) ).
thf(f12039,plain,
( spl155_528
| ~ spl155_86
| ~ spl155_149 ),
inference(avatar_split_clause,[],[f4288,f4212,f3289,f12037]) ).
thf(f12037,plain,
( spl155_528
<=> ! [X2: nat,X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X1) = X0 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP5,X0),X2),X1) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP4,X1),X0),X2) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP3,X2),X1),X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP2,X1),X2),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_528])]) ).
thf(f4288,plain,
( ! [X2: nat,X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X1) = X0 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP5,X0),X2),X1) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP4,X1),X0),X2) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP3,X2),X1),X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP2,X1),X2),X0) ) )
| ~ spl155_86
| ~ spl155_149 ),
inference(trivial_inequality_removal,[],[f4219]) ).
thf(f4219,plain,
( ! [X2: nat,X0: nat,X1: nat] :
( ( $true != $true )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X1) = X0 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP5,X0),X2),X1) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP4,X1),X0),X2) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP3,X2),X1),X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP2,X1),X2),X0) ) )
| ~ spl155_86
| ~ spl155_149 ),
inference(superposition,[],[f3290,f4213]) ).
thf(f11949,plain,
( spl155_527
| ~ spl155_2
| ~ spl155_53 ),
inference(avatar_split_clause,[],[f3132,f3126,f2739,f11947]) ).
thf(f11947,plain,
( spl155_527
<=> ! [X2: nat,X0: list_P559422087at_nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,nat)),sK65,X0),X1),X2)),vAPP(nat,list_P559422087at_nat,vAPP(nat,sTfun(nat,list_P559422087at_nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,list_P559422087at_nat)),sK66,X0),X1),X2)),X2) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,$o)),sP7,X0),X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_527])]) ).
thf(f3126,plain,
( spl155_53
<=> ! [X2: list_P559422087at_nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,nat)),sK65,X2),X1),X0)),vAPP(nat,list_P559422087at_nat,vAPP(nat,sTfun(nat,list_P559422087at_nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,list_P559422087at_nat)),sK66,X2),X1),X0)),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,$o)),sP7,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_53])]) ).
thf(f3132,plain,
( ! [X2: nat,X0: list_P559422087at_nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,nat)),sK65,X0),X1),X2)),vAPP(nat,list_P559422087at_nat,vAPP(nat,sTfun(nat,list_P559422087at_nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,list_P559422087at_nat)),sK66,X0),X1),X2)),X2) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,$o)),sP7,X0),X1),X2) ) )
| ~ spl155_2
| ~ spl155_53 ),
inference(trivial_inequality_removal,[],[f3131]) ).
thf(f3131,plain,
( ! [X2: nat,X0: list_P559422087at_nat,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,nat)),sK65,X0),X1),X2)),vAPP(nat,list_P559422087at_nat,vAPP(nat,sTfun(nat,list_P559422087at_nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,list_P559422087at_nat)),sK66,X0),X1),X2)),X2) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,$o)),sP7,X0),X1),X2) ) )
| ~ spl155_2
| ~ spl155_53 ),
inference(superposition,[],[f3127,f2740]) ).
thf(f3127,plain,
( ! [X2: list_P559422087at_nat,X0: nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,$o)),sP7,X2),X1),X0) )
| ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,nat)),sK65,X2),X1),X0)),vAPP(nat,list_P559422087at_nat,vAPP(nat,sTfun(nat,list_P559422087at_nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,list_P559422087at_nat)),sK66,X2),X1),X0)),X0) ) )
| ~ spl155_53 ),
inference(avatar_component_clause,[],[f3126]) ).
thf(f11945,plain,
( spl155_526
| ~ spl155_2
| ~ spl155_52 ),
inference(avatar_split_clause,[],[f3130,f3122,f2739,f11943]) ).
thf(f11943,plain,
( spl155_526
<=> ! [X2: nat,X0: list_P559422087at_nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,nat)),sK63,X0),X1),X2)),vAPP(nat,list_P559422087at_nat,vAPP(nat,sTfun(nat,list_P559422087at_nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,list_P559422087at_nat)),sK62,X0),X1),X2)),X2) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,$o)),sP6,X0),X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_526])]) ).
thf(f3122,plain,
( spl155_52
<=> ! [X2: list_P559422087at_nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,nat)),sK63,X2),X1),X0)),vAPP(nat,list_P559422087at_nat,vAPP(nat,sTfun(nat,list_P559422087at_nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,list_P559422087at_nat)),sK62,X2),X1),X0)),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,$o)),sP6,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_52])]) ).
thf(f3130,plain,
( ! [X2: nat,X0: list_P559422087at_nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,nat)),sK63,X0),X1),X2)),vAPP(nat,list_P559422087at_nat,vAPP(nat,sTfun(nat,list_P559422087at_nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,list_P559422087at_nat)),sK62,X0),X1),X2)),X2) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,$o)),sP6,X0),X1),X2) ) )
| ~ spl155_2
| ~ spl155_52 ),
inference(trivial_inequality_removal,[],[f3129]) ).
thf(f3129,plain,
( ! [X2: nat,X0: list_P559422087at_nat,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,nat)),sK63,X0),X1),X2)),vAPP(nat,list_P559422087at_nat,vAPP(nat,sTfun(nat,list_P559422087at_nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,list_P559422087at_nat)),sK62,X0),X1),X2)),X2) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,$o)),sP6,X0),X1),X2) ) )
| ~ spl155_2
| ~ spl155_52 ),
inference(superposition,[],[f3123,f2740]) ).
thf(f3123,plain,
( ! [X2: list_P559422087at_nat,X0: nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,$o)),sP6,X2),X1),X0) )
| ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,nat)),sK63,X2),X1),X0)),vAPP(nat,list_P559422087at_nat,vAPP(nat,sTfun(nat,list_P559422087at_nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,list_P559422087at_nat)),sK62,X2),X1),X0)),X0) ) )
| ~ spl155_52 ),
inference(avatar_component_clause,[],[f3122]) ).
thf(f11937,plain,
( spl155_525
| ~ spl155_119
| ~ spl155_145 ),
inference(avatar_split_clause,[],[f4059,f4027,f3632,f11935]) ).
thf(f11935,plain,
( spl155_525
<=> ! [X2: set_Pr1986765409at_nat,X0: set_Pr1986765409at_nat,X1: set_se1612935105at_nat] :
( ( vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK21,X0),X1) = X2 )
| ( $true != vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X2),X1) )
| ( $true != vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X0),X1) )
| ( $true != vAPP(set_se1612935105at_nat,$o,finite1457549322at_nat,X1) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,X2),vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK21,X0),X1))),vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK21,X0),X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_525])]) ).
thf(f4027,plain,
( spl155_145
<=> ! [X0: set_se1612935105at_nat,X1: set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat] :
( ( vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK21,X1),X0) = X3 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK21,X1),X0)),X3) )
| ( $true != vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X3),X0) )
| ( $true != vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X1),X0) )
| ( $true != vAPP(set_se1612935105at_nat,$o,finite1457549322at_nat,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_145])]) ).
thf(f4059,plain,
( ! [X2: set_Pr1986765409at_nat,X0: set_Pr1986765409at_nat,X1: set_se1612935105at_nat] :
( ( vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK21,X0),X1) = X2 )
| ( $true != vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X2),X1) )
| ( $true != vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X0),X1) )
| ( $true != vAPP(set_se1612935105at_nat,$o,finite1457549322at_nat,X1) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,X2),vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK21,X0),X1))),vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK21,X0),X1)) ) )
| ~ spl155_119
| ~ spl155_145 ),
inference(trivial_inequality_removal,[],[f4056]) ).
thf(f4056,plain,
( ! [X2: set_Pr1986765409at_nat,X0: set_Pr1986765409at_nat,X1: set_se1612935105at_nat] :
( ( $true != $true )
| ( vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK21,X0),X1) = X2 )
| ( $true != vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X2),X1) )
| ( $true != vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X0),X1) )
| ( $true != vAPP(set_se1612935105at_nat,$o,finite1457549322at_nat,X1) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,X2),vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK21,X0),X1))),vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK21,X0),X1)) ) )
| ~ spl155_119
| ~ spl155_145 ),
inference(superposition,[],[f4028,f3633]) ).
thf(f4028,plain,
( ! [X3: set_Pr1986765409at_nat,X0: set_se1612935105at_nat,X1: set_Pr1986765409at_nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK21,X1),X0)),X3) )
| ( vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK21,X1),X0) = X3 )
| ( $true != vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X3),X0) )
| ( $true != vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X1),X0) )
| ( $true != vAPP(set_se1612935105at_nat,$o,finite1457549322at_nat,X0) ) )
| ~ spl155_145 ),
inference(avatar_component_clause,[],[f4027]) ).
thf(f11933,plain,
( spl155_524
| ~ spl155_117
| ~ spl155_141 ),
inference(avatar_split_clause,[],[f4034,f4010,f3624,f11931]) ).
thf(f11931,plain,
( spl155_524
<=> ! [X2: set_nat,X0: set_nat,X1: set_set_nat] :
( ( vAPP(set_set_nat,set_nat,vAPP(set_nat,sTfun(set_set_nat,set_nat),sK18,X0),X1) = X2 )
| ( $true != vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X2),X1) )
| ( $true != vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X0),X1) )
| ( $true != vAPP(set_set_nat,$o,finite2012248349et_nat,X1) )
| ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,vAPP(set_nat,nat,vAPP(set_nat,sTfun(set_nat,nat),sK15,X2),vAPP(set_set_nat,set_nat,vAPP(set_nat,sTfun(set_set_nat,set_nat),sK18,X0),X1))),vAPP(set_set_nat,set_nat,vAPP(set_nat,sTfun(set_set_nat,set_nat),sK18,X0),X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_524])]) ).
thf(f4010,plain,
( spl155_141
<=> ! [X0: set_set_nat,X1: set_nat,X3: set_nat] :
( ( vAPP(set_set_nat,set_nat,vAPP(set_nat,sTfun(set_set_nat,set_nat),sK18,X1),X0) = X3 )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_set_nat,set_nat,vAPP(set_nat,sTfun(set_set_nat,set_nat),sK18,X1),X0)),X3) )
| ( $true != vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X3),X0) )
| ( $true != vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X1),X0) )
| ( $true != vAPP(set_set_nat,$o,finite2012248349et_nat,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_141])]) ).
thf(f4034,plain,
( ! [X2: set_nat,X0: set_nat,X1: set_set_nat] :
( ( vAPP(set_set_nat,set_nat,vAPP(set_nat,sTfun(set_set_nat,set_nat),sK18,X0),X1) = X2 )
| ( $true != vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X2),X1) )
| ( $true != vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X0),X1) )
| ( $true != vAPP(set_set_nat,$o,finite2012248349et_nat,X1) )
| ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,vAPP(set_nat,nat,vAPP(set_nat,sTfun(set_nat,nat),sK15,X2),vAPP(set_set_nat,set_nat,vAPP(set_nat,sTfun(set_set_nat,set_nat),sK18,X0),X1))),vAPP(set_set_nat,set_nat,vAPP(set_nat,sTfun(set_set_nat,set_nat),sK18,X0),X1)) ) )
| ~ spl155_117
| ~ spl155_141 ),
inference(trivial_inequality_removal,[],[f4031]) ).
thf(f4031,plain,
( ! [X2: set_nat,X0: set_nat,X1: set_set_nat] :
( ( $true != $true )
| ( vAPP(set_set_nat,set_nat,vAPP(set_nat,sTfun(set_set_nat,set_nat),sK18,X0),X1) = X2 )
| ( $true != vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X2),X1) )
| ( $true != vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X0),X1) )
| ( $true != vAPP(set_set_nat,$o,finite2012248349et_nat,X1) )
| ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,vAPP(set_nat,nat,vAPP(set_nat,sTfun(set_nat,nat),sK15,X2),vAPP(set_set_nat,set_nat,vAPP(set_nat,sTfun(set_set_nat,set_nat),sK18,X0),X1))),vAPP(set_set_nat,set_nat,vAPP(set_nat,sTfun(set_set_nat,set_nat),sK18,X0),X1)) ) )
| ~ spl155_117
| ~ spl155_141 ),
inference(superposition,[],[f4011,f3625]) ).
thf(f4011,plain,
( ! [X3: set_nat,X0: set_set_nat,X1: set_nat] :
( ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_set_nat,set_nat,vAPP(set_nat,sTfun(set_set_nat,set_nat),sK18,X1),X0)),X3) )
| ( vAPP(set_set_nat,set_nat,vAPP(set_nat,sTfun(set_set_nat,set_nat),sK18,X1),X0) = X3 )
| ( $true != vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X3),X0) )
| ( $true != vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X1),X0) )
| ( $true != vAPP(set_set_nat,$o,finite2012248349et_nat,X0) ) )
| ~ spl155_141 ),
inference(avatar_component_clause,[],[f4010]) ).
thf(f11923,plain,
( spl155_523
| ~ spl155_181
| ~ spl155_466 ),
inference(avatar_split_clause,[],[f10139,f10040,f4909,f11921]) ).
thf(f11921,plain,
( spl155_523
<=> ! [X0: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),edges)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,X0),edges)),edges) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_523])]) ).
thf(f10139,plain,
( ! [X0: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),edges)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,X0),edges)),edges) ) )
| ~ spl155_181
| ~ spl155_466 ),
inference(trivial_inequality_removal,[],[f10104]) ).
thf(f10104,plain,
( ! [X0: set_Pr1986765409at_nat] :
( ( $true != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),edges)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,X0),edges)),edges) ) )
| ~ spl155_181
| ~ spl155_466 ),
inference(superposition,[],[f4910,f10041]) ).
thf(f11891,plain,
( spl155_522
| ~ spl155_76
| ~ spl155_144 ),
inference(avatar_split_clause,[],[f4054,f4023,f3244,f11889]) ).
thf(f11889,plain,
( spl155_522
<=> ! [X2: set_Pr1986765409at_nat,X0: set_Pr1986765409at_nat,X1: set_se1612935105at_nat] :
( ( vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK20,X0),X1) = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK20,X0),X1)),X2) )
| ( $true != vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK20,X0),X1)),X2)),X1) )
| ( $true != vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X0),X1) )
| ( $true != vAPP(set_se1612935105at_nat,$o,finite1457549322at_nat,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_522])]) ).
thf(f4054,plain,
( ! [X2: set_Pr1986765409at_nat,X0: set_Pr1986765409at_nat,X1: set_se1612935105at_nat] :
( ( vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK20,X0),X1) = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK20,X0),X1)),X2) )
| ( $true != vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK20,X0),X1)),X2)),X1) )
| ( $true != vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X0),X1) )
| ( $true != vAPP(set_se1612935105at_nat,$o,finite1457549322at_nat,X1) ) )
| ~ spl155_76
| ~ spl155_144 ),
inference(trivial_inequality_removal,[],[f4045]) ).
thf(f4045,plain,
( ! [X2: set_Pr1986765409at_nat,X0: set_Pr1986765409at_nat,X1: set_se1612935105at_nat] :
( ( $true != $true )
| ( vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK20,X0),X1) = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK20,X0),X1)),X2) )
| ( $true != vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK20,X0),X1)),X2)),X1) )
| ( $true != vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X0),X1) )
| ( $true != vAPP(set_se1612935105at_nat,$o,finite1457549322at_nat,X1) ) )
| ~ spl155_76
| ~ spl155_144 ),
inference(superposition,[],[f4024,f3245]) ).
thf(f11887,plain,
( spl155_521
| ~ spl155_77
| ~ spl155_144 ),
inference(avatar_split_clause,[],[f4053,f4023,f3248,f11885]) ).
thf(f11885,plain,
( spl155_521
<=> ! [X2: set_se1612935105at_nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK20,X1),X2) = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK20,X1),X2)) )
| ( $true != vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK20,X1),X2))),X2) )
| ( $true != vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X1),X2) )
| ( vAPP(set_se1612935105at_nat,$o,finite1457549322at_nat,X2) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_521])]) ).
thf(f4053,plain,
( ! [X2: set_se1612935105at_nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK20,X1),X2) = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK20,X1),X2)) )
| ( $true != vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK20,X1),X2))),X2) )
| ( $true != vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X1),X2) )
| ( vAPP(set_se1612935105at_nat,$o,finite1457549322at_nat,X2) != $true ) )
| ~ spl155_77
| ~ spl155_144 ),
inference(trivial_inequality_removal,[],[f4046]) ).
thf(f4046,plain,
( ! [X2: set_se1612935105at_nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true != $true )
| ( vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK20,X1),X2) = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK20,X1),X2)) )
| ( $true != vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK20,X1),X2))),X2) )
| ( $true != vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X1),X2) )
| ( vAPP(set_se1612935105at_nat,$o,finite1457549322at_nat,X2) != $true ) )
| ~ spl155_77
| ~ spl155_144 ),
inference(superposition,[],[f4024,f3249]) ).
thf(f11883,plain,
( spl155_520
| ~ spl155_73
| ~ spl155_142 ),
inference(avatar_split_clause,[],[f4043,f4014,f3232,f11881]) ).
thf(f11881,plain,
( spl155_520
<=> ! [X2: set_nat,X0: set_nat,X1: set_set_nat] :
( ( vAPP(set_set_nat,set_nat,vAPP(set_nat,sTfun(set_set_nat,set_nat),sK19,X0),X1) = vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,vAPP(set_set_nat,set_nat,vAPP(set_nat,sTfun(set_set_nat,set_nat),sK19,X0),X1)),X2) )
| ( $true != vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,vAPP(set_set_nat,set_nat,vAPP(set_nat,sTfun(set_set_nat,set_nat),sK19,X0),X1)),X2)),X1) )
| ( $true != vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X0),X1) )
| ( $true != vAPP(set_set_nat,$o,finite2012248349et_nat,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_520])]) ).
thf(f4014,plain,
( spl155_142
<=> ! [X0: set_set_nat,X1: set_nat,X3: set_nat] :
( ( vAPP(set_set_nat,set_nat,vAPP(set_nat,sTfun(set_set_nat,set_nat),sK19,X1),X0) = X3 )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X3),vAPP(set_set_nat,set_nat,vAPP(set_nat,sTfun(set_set_nat,set_nat),sK19,X1),X0)) )
| ( $true != vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X3),X0) )
| ( $true != vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X1),X0) )
| ( $true != vAPP(set_set_nat,$o,finite2012248349et_nat,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_142])]) ).
thf(f4043,plain,
( ! [X2: set_nat,X0: set_nat,X1: set_set_nat] :
( ( vAPP(set_set_nat,set_nat,vAPP(set_nat,sTfun(set_set_nat,set_nat),sK19,X0),X1) = vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,vAPP(set_set_nat,set_nat,vAPP(set_nat,sTfun(set_set_nat,set_nat),sK19,X0),X1)),X2) )
| ( $true != vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,vAPP(set_set_nat,set_nat,vAPP(set_nat,sTfun(set_set_nat,set_nat),sK19,X0),X1)),X2)),X1) )
| ( $true != vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X0),X1) )
| ( $true != vAPP(set_set_nat,$o,finite2012248349et_nat,X1) ) )
| ~ spl155_73
| ~ spl155_142 ),
inference(trivial_inequality_removal,[],[f4036]) ).
thf(f4036,plain,
( ! [X2: set_nat,X0: set_nat,X1: set_set_nat] :
( ( $true != $true )
| ( vAPP(set_set_nat,set_nat,vAPP(set_nat,sTfun(set_set_nat,set_nat),sK19,X0),X1) = vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,vAPP(set_set_nat,set_nat,vAPP(set_nat,sTfun(set_set_nat,set_nat),sK19,X0),X1)),X2) )
| ( $true != vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,vAPP(set_set_nat,set_nat,vAPP(set_nat,sTfun(set_set_nat,set_nat),sK19,X0),X1)),X2)),X1) )
| ( $true != vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X0),X1) )
| ( $true != vAPP(set_set_nat,$o,finite2012248349et_nat,X1) ) )
| ~ spl155_73
| ~ spl155_142 ),
inference(superposition,[],[f4015,f3233]) ).
thf(f4015,plain,
( ! [X3: set_nat,X0: set_set_nat,X1: set_nat] :
( ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X3),vAPP(set_set_nat,set_nat,vAPP(set_nat,sTfun(set_set_nat,set_nat),sK19,X1),X0)) )
| ( vAPP(set_set_nat,set_nat,vAPP(set_nat,sTfun(set_set_nat,set_nat),sK19,X1),X0) = X3 )
| ( $true != vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X3),X0) )
| ( $true != vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X1),X0) )
| ( $true != vAPP(set_set_nat,$o,finite2012248349et_nat,X0) ) )
| ~ spl155_142 ),
inference(avatar_component_clause,[],[f4014]) ).
thf(f11879,plain,
( spl155_519
| ~ spl155_72
| ~ spl155_142 ),
inference(avatar_split_clause,[],[f4042,f4014,f3228,f11877]) ).
thf(f11877,plain,
( spl155_519
<=> ! [X2: set_set_nat,X0: set_nat,X1: set_nat] :
( ( vAPP(set_set_nat,set_nat,vAPP(set_nat,sTfun(set_set_nat,set_nat),sK19,X1),X2) = vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),vAPP(set_set_nat,set_nat,vAPP(set_nat,sTfun(set_set_nat,set_nat),sK19,X1),X2)) )
| ( $true != vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),vAPP(set_set_nat,set_nat,vAPP(set_nat,sTfun(set_set_nat,set_nat),sK19,X1),X2))),X2) )
| ( $true != vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X1),X2) )
| ( vAPP(set_set_nat,$o,finite2012248349et_nat,X2) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_519])]) ).
thf(f4042,plain,
( ! [X2: set_set_nat,X0: set_nat,X1: set_nat] :
( ( vAPP(set_set_nat,set_nat,vAPP(set_nat,sTfun(set_set_nat,set_nat),sK19,X1),X2) = vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),vAPP(set_set_nat,set_nat,vAPP(set_nat,sTfun(set_set_nat,set_nat),sK19,X1),X2)) )
| ( $true != vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),vAPP(set_set_nat,set_nat,vAPP(set_nat,sTfun(set_set_nat,set_nat),sK19,X1),X2))),X2) )
| ( $true != vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X1),X2) )
| ( vAPP(set_set_nat,$o,finite2012248349et_nat,X2) != $true ) )
| ~ spl155_72
| ~ spl155_142 ),
inference(trivial_inequality_removal,[],[f4037]) ).
thf(f4037,plain,
( ! [X2: set_set_nat,X0: set_nat,X1: set_nat] :
( ( $true != $true )
| ( vAPP(set_set_nat,set_nat,vAPP(set_nat,sTfun(set_set_nat,set_nat),sK19,X1),X2) = vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),vAPP(set_set_nat,set_nat,vAPP(set_nat,sTfun(set_set_nat,set_nat),sK19,X1),X2)) )
| ( $true != vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),vAPP(set_set_nat,set_nat,vAPP(set_nat,sTfun(set_set_nat,set_nat),sK19,X1),X2))),X2) )
| ( $true != vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X1),X2) )
| ( vAPP(set_set_nat,$o,finite2012248349et_nat,X2) != $true ) )
| ~ spl155_72
| ~ spl155_142 ),
inference(superposition,[],[f4015,f3229]) ).
thf(f11875,plain,
( spl155_518
| ~ spl155_2
| ~ spl155_50 ),
inference(avatar_split_clause,[],[f3115,f3111,f2739,f11873]) ).
thf(f11873,plain,
( spl155_518
<=> ! [X2: nat,X0: list_P559422087at_nat,X1: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,nat)),sK64,X0),X1),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,nat)),sK65,X0),X1),X2))),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,$o)),sP7,X0),X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_518])]) ).
thf(f3111,plain,
( spl155_50
<=> ! [X2: list_P559422087at_nat,X0: nat,X1: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,nat)),sK64,X2),X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,nat)),sK65,X2),X1),X0))),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,$o)),sP7,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_50])]) ).
thf(f3115,plain,
( ! [X2: nat,X0: list_P559422087at_nat,X1: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,nat)),sK64,X0),X1),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,nat)),sK65,X0),X1),X2))),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,$o)),sP7,X0),X1),X2) ) )
| ~ spl155_2
| ~ spl155_50 ),
inference(trivial_inequality_removal,[],[f3114]) ).
thf(f3114,plain,
( ! [X2: nat,X0: list_P559422087at_nat,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,nat)),sK64,X0),X1),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,nat)),sK65,X0),X1),X2))),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,$o)),sP7,X0),X1),X2) ) )
| ~ spl155_2
| ~ spl155_50 ),
inference(superposition,[],[f3112,f2740]) ).
thf(f3112,plain,
( ! [X2: list_P559422087at_nat,X0: nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,$o)),sP7,X2),X1),X0) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,nat)),sK64,X2),X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,nat)),sK65,X2),X1),X0))),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) ) )
| ~ spl155_50 ),
inference(avatar_component_clause,[],[f3111]) ).
thf(f11870,plain,
( spl155_517
| ~ spl155_23
| ~ spl155_466 ),
inference(avatar_split_clause,[],[f10128,f10040,f2899,f11868]) ).
thf(f2899,plain,
( spl155_23
<=> ! [X2: set_Pr1986765409at_nat,X0: product_prod_nat_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),X2) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_23])]) ).
thf(f10128,plain,
( ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),X1) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1)),edges)),edges) ) )
| ~ spl155_23
| ~ spl155_466 ),
inference(trivial_inequality_removal,[],[f10115]) ).
thf(f10115,plain,
( ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),X1) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1)),edges)),edges) ) )
| ~ spl155_23
| ~ spl155_466 ),
inference(superposition,[],[f2900,f10041]) ).
thf(f2900,plain,
( ! [X2: set_Pr1986765409at_nat,X0: product_prod_nat_nat,X1: set_Pr1986765409at_nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),X2)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),X2) ) )
| ~ spl155_23 ),
inference(avatar_component_clause,[],[f2899]) ).
thf(f11866,plain,
( spl155_516
| ~ spl155_2
| ~ spl155_49 ),
inference(avatar_split_clause,[],[f3109,f3105,f2739,f11864]) ).
thf(f11864,plain,
( spl155_516
<=> ! [X2: nat,X0: list_P559422087at_nat,X1: nat] :
( ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,nat)),sK63,X0),X1),X2))),vAPP(nat,list_P559422087at_nat,vAPP(nat,sTfun(nat,list_P559422087at_nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,list_P559422087at_nat)),sK62,X0),X1),X2)) = X0 )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,$o)),sP6,X0),X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_516])]) ).
thf(f3105,plain,
( spl155_49
<=> ! [X2: list_P559422087at_nat,X0: nat,X1: nat] :
( ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,nat)),sK63,X2),X1),X0))),vAPP(nat,list_P559422087at_nat,vAPP(nat,sTfun(nat,list_P559422087at_nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,list_P559422087at_nat)),sK62,X2),X1),X0)) = X2 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,$o)),sP6,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_49])]) ).
thf(f3109,plain,
( ! [X2: nat,X0: list_P559422087at_nat,X1: nat] :
( ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,nat)),sK63,X0),X1),X2))),vAPP(nat,list_P559422087at_nat,vAPP(nat,sTfun(nat,list_P559422087at_nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,list_P559422087at_nat)),sK62,X0),X1),X2)) = X0 )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,$o)),sP6,X0),X1),X2) ) )
| ~ spl155_2
| ~ spl155_49 ),
inference(trivial_inequality_removal,[],[f3108]) ).
thf(f3108,plain,
( ! [X2: nat,X0: list_P559422087at_nat,X1: nat] :
( ( $true != $true )
| ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,nat)),sK63,X0),X1),X2))),vAPP(nat,list_P559422087at_nat,vAPP(nat,sTfun(nat,list_P559422087at_nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,list_P559422087at_nat)),sK62,X0),X1),X2)) = X0 )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,$o)),sP6,X0),X1),X2) ) )
| ~ spl155_2
| ~ spl155_49 ),
inference(superposition,[],[f3106,f2740]) ).
thf(f3106,plain,
( ! [X2: list_P559422087at_nat,X0: nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,$o)),sP6,X2),X1),X0) )
| ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,nat)),sK63,X2),X1),X0))),vAPP(nat,list_P559422087at_nat,vAPP(nat,sTfun(nat,list_P559422087at_nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,list_P559422087at_nat)),sK62,X2),X1),X0)) = X2 ) )
| ~ spl155_49 ),
inference(avatar_component_clause,[],[f3105]) ).
thf(f11376,plain,
( spl155_515
| ~ spl155_87
| ~ spl155_147 ),
inference(avatar_split_clause,[],[f4141,f4065,f3293,f11374]) ).
thf(f11374,plain,
( spl155_515
<=> ! [X2: nat,X0: nat > nat > $o,X1: nat] :
( ( vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK37,X0) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK38,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK37,X0)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK36,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_515])]) ).
thf(f4065,plain,
( spl155_147
<=> ! [X2: nat,X0: nat > nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK36,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,X0)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK37,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK38,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_147])]) ).
thf(f4141,plain,
( ! [X2: nat,X0: nat > nat > $o,X1: nat] :
( ( vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK37,X0) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK38,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK37,X0)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK36,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,X0)) ) )
| ~ spl155_87
| ~ spl155_147 ),
inference(trivial_inequality_removal,[],[f4126]) ).
thf(f4126,plain,
( ! [X2: nat,X0: nat > nat > $o,X1: nat] :
( ( $true != $true )
| ( vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK37,X0) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK38,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK37,X0)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK36,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,X0)) ) )
| ~ spl155_87
| ~ spl155_147 ),
inference(superposition,[],[f3294,f4066]) ).
thf(f4066,plain,
( ! [X2: nat,X0: nat > nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK36,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,X0)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK37,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK38,X0)) ) )
| ~ spl155_147 ),
inference(avatar_component_clause,[],[f4065]) ).
thf(f11372,plain,
( spl155_514
| ~ spl155_86
| ~ spl155_147 ),
inference(avatar_split_clause,[],[f4140,f4065,f3289,f11370]) ).
thf(f11370,plain,
( spl155_514
<=> ! [X2: nat,X0: nat > nat > $o,X1: nat] :
( ( vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK37,X0) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK37,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK38,X0)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK36,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_514])]) ).
thf(f4140,plain,
( ! [X2: nat,X0: nat > nat > $o,X1: nat] :
( ( vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK37,X0) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK37,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK38,X0)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK36,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,X0)) ) )
| ~ spl155_86
| ~ spl155_147 ),
inference(trivial_inequality_removal,[],[f4127]) ).
thf(f4127,plain,
( ! [X2: nat,X0: nat > nat > $o,X1: nat] :
( ( $true != $true )
| ( vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK37,X0) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK37,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK38,X0)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK36,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,X0)) ) )
| ~ spl155_86
| ~ spl155_147 ),
inference(superposition,[],[f3290,f4066]) ).
thf(f11368,plain,
( spl155_513
| ~ spl155_119
| ~ spl155_144 ),
inference(avatar_split_clause,[],[f4051,f4023,f3632,f11366]) ).
thf(f11366,plain,
( spl155_513
<=> ! [X2: set_se1612935105at_nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK20,X1),X2) = X0 )
| ( $true != vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X0),X2) )
| ( $true != vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X1),X2) )
| ( vAPP(set_se1612935105at_nat,$o,finite1457549322at_nat,X2) != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK20,X1),X2)),X0)),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_513])]) ).
thf(f4051,plain,
( ! [X2: set_se1612935105at_nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK20,X1),X2) = X0 )
| ( $true != vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X0),X2) )
| ( $true != vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X1),X2) )
| ( vAPP(set_se1612935105at_nat,$o,finite1457549322at_nat,X2) != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK20,X1),X2)),X0)),X0) ) )
| ~ spl155_119
| ~ spl155_144 ),
inference(trivial_inequality_removal,[],[f4048]) ).
thf(f4048,plain,
( ! [X2: set_se1612935105at_nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true != $true )
| ( vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK20,X1),X2) = X0 )
| ( $true != vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X0),X2) )
| ( $true != vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X1),X2) )
| ( vAPP(set_se1612935105at_nat,$o,finite1457549322at_nat,X2) != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK20,X1),X2)),X0)),X0) ) )
| ~ spl155_119
| ~ spl155_144 ),
inference(superposition,[],[f4024,f3633]) ).
thf(f11364,plain,
( spl155_512
| ~ spl155_117
| ~ spl155_142 ),
inference(avatar_split_clause,[],[f4041,f4014,f3624,f11362]) ).
thf(f11362,plain,
( spl155_512
<=> ! [X2: set_set_nat,X0: set_nat,X1: set_nat] :
( ( vAPP(set_set_nat,set_nat,vAPP(set_nat,sTfun(set_set_nat,set_nat),sK19,X1),X2) = X0 )
| ( $true != vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X0),X2) )
| ( $true != vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X1),X2) )
| ( vAPP(set_set_nat,$o,finite2012248349et_nat,X2) != $true )
| ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,vAPP(set_nat,nat,vAPP(set_nat,sTfun(set_nat,nat),sK15,vAPP(set_set_nat,set_nat,vAPP(set_nat,sTfun(set_set_nat,set_nat),sK19,X1),X2)),X0)),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_512])]) ).
thf(f4041,plain,
( ! [X2: set_set_nat,X0: set_nat,X1: set_nat] :
( ( vAPP(set_set_nat,set_nat,vAPP(set_nat,sTfun(set_set_nat,set_nat),sK19,X1),X2) = X0 )
| ( $true != vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X0),X2) )
| ( $true != vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X1),X2) )
| ( vAPP(set_set_nat,$o,finite2012248349et_nat,X2) != $true )
| ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,vAPP(set_nat,nat,vAPP(set_nat,sTfun(set_nat,nat),sK15,vAPP(set_set_nat,set_nat,vAPP(set_nat,sTfun(set_set_nat,set_nat),sK19,X1),X2)),X0)),X0) ) )
| ~ spl155_117
| ~ spl155_142 ),
inference(trivial_inequality_removal,[],[f4038]) ).
thf(f4038,plain,
( ! [X2: set_set_nat,X0: set_nat,X1: set_nat] :
( ( $true != $true )
| ( vAPP(set_set_nat,set_nat,vAPP(set_nat,sTfun(set_set_nat,set_nat),sK19,X1),X2) = X0 )
| ( $true != vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X0),X2) )
| ( $true != vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X1),X2) )
| ( vAPP(set_set_nat,$o,finite2012248349et_nat,X2) != $true )
| ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,vAPP(set_nat,nat,vAPP(set_nat,sTfun(set_nat,nat),sK15,vAPP(set_set_nat,set_nat,vAPP(set_nat,sTfun(set_set_nat,set_nat),sK19,X1),X2)),X0)),X0) ) )
| ~ spl155_117
| ~ spl155_142 ),
inference(superposition,[],[f4015,f3625]) ).
thf(f11360,plain,
( spl155_511
| ~ spl155_22
| ~ spl155_466 ),
inference(avatar_split_clause,[],[f10127,f10040,f2895,f11358]) ).
thf(f2895,plain,
( spl155_22
<=> ! [X2: set_Pr1986765409at_nat,X0: product_prod_nat_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),X1) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_22])]) ).
thf(f10127,plain,
( ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),X0) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1)),edges)),edges) ) )
| ~ spl155_22
| ~ spl155_466 ),
inference(trivial_inequality_removal,[],[f10116]) ).
thf(f10116,plain,
( ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),X0) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1)),edges)),edges) ) )
| ~ spl155_22
| ~ spl155_466 ),
inference(superposition,[],[f2896,f10041]) ).
thf(f2896,plain,
( ! [X2: set_Pr1986765409at_nat,X0: product_prod_nat_nat,X1: set_Pr1986765409at_nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),X2)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),X1) ) )
| ~ spl155_22 ),
inference(avatar_component_clause,[],[f2895]) ).
thf(f11356,plain,
( spl155_510
| ~ spl155_2
| ~ spl155_48 ),
inference(avatar_split_clause,[],[f3103,f3099,f2739,f11354]) ).
thf(f11354,plain,
( spl155_510
<=> ! [X0: nat,X3: nat,X2: product_prod_nat_nat > a,X1: nat] :
( ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X1),vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),reachableNodes_a,X2),X3)) )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),reachableNodes_a,X2),X3)) )
| ( $false = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X0),X1)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_510])]) ).
thf(f3099,plain,
( spl155_48
<=> ! [X0: nat,X3: nat,X2: nat,X1: product_prod_nat_nat > a] :
( ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X3),vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),reachableNodes_a,X1),X2)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X0),X3)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X1)) )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),reachableNodes_a,X1),X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_48])]) ).
thf(f3103,plain,
( ! [X2: product_prod_nat_nat > a,X3: nat,X0: nat,X1: nat] :
( ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X1),vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),reachableNodes_a,X2),X3)) )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),reachableNodes_a,X2),X3)) )
| ( $false = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X0),X1)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X2)) ) )
| ~ spl155_2
| ~ spl155_48 ),
inference(trivial_inequality_removal,[],[f3102]) ).
thf(f3102,plain,
( ! [X2: product_prod_nat_nat > a,X3: nat,X0: nat,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X1),vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),reachableNodes_a,X2),X3)) )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),reachableNodes_a,X2),X3)) )
| ( $false = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X0),X1)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X2)) ) )
| ~ spl155_2
| ~ spl155_48 ),
inference(superposition,[],[f3100,f2740]) ).
thf(f3100,plain,
( ! [X2: nat,X3: nat,X0: nat,X1: product_prod_nat_nat > a] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X0),X3)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X1)) )
| ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X3),vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),reachableNodes_a,X1),X2)) )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),reachableNodes_a,X1),X2)) ) )
| ~ spl155_48 ),
inference(avatar_component_clause,[],[f3099]) ).
thf(f11349,plain,
( spl155_509
| ~ spl155_102
| ~ spl155_135 ),
inference(avatar_split_clause,[],[f3874,f3836,f3476,f11347]) ).
thf(f11347,plain,
( spl155_509
<=> ! [X0: product_prod_nat_nat > $o,X1: product_prod_nat_nat > $o] :
( ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X1)) != vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X0)) )
| ( vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X0) = vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X1) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X1)) )
| ( $true = vAPP(product_prod_nat_nat,$o,X0,vAPP(sTfun(product_prod_nat_nat,$o),product_prod_nat_nat,vAPP(sTfun(product_prod_nat_nat,$o),sTfun(sTfun(product_prod_nat_nat,$o),product_prod_nat_nat),sK12,X1),X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_509])]) ).
thf(f3836,plain,
( spl155_135
<=> ! [X0: product_prod_nat_nat > $o,X1: product_prod_nat_nat > $o] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X0)),vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X1)) )
| ( $true = vAPP(product_prod_nat_nat,$o,X0,vAPP(sTfun(product_prod_nat_nat,$o),product_prod_nat_nat,vAPP(sTfun(product_prod_nat_nat,$o),sTfun(sTfun(product_prod_nat_nat,$o),product_prod_nat_nat),sK12,X1),X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_135])]) ).
thf(f3874,plain,
( ! [X0: product_prod_nat_nat > $o,X1: product_prod_nat_nat > $o] :
( ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X1)) != vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X0)) )
| ( vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X0) = vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X1) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X1)) )
| ( $true = vAPP(product_prod_nat_nat,$o,X0,vAPP(sTfun(product_prod_nat_nat,$o),product_prod_nat_nat,vAPP(sTfun(product_prod_nat_nat,$o),sTfun(sTfun(product_prod_nat_nat,$o),product_prod_nat_nat),sK12,X1),X0)) ) )
| ~ spl155_102
| ~ spl155_135 ),
inference(trivial_inequality_removal,[],[f3864]) ).
thf(f3864,plain,
( ! [X0: product_prod_nat_nat > $o,X1: product_prod_nat_nat > $o] :
( ( $true != $true )
| ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X1)) != vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X0)) )
| ( vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X0) = vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X1) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X1)) )
| ( $true = vAPP(product_prod_nat_nat,$o,X0,vAPP(sTfun(product_prod_nat_nat,$o),product_prod_nat_nat,vAPP(sTfun(product_prod_nat_nat,$o),sTfun(sTfun(product_prod_nat_nat,$o),product_prod_nat_nat),sK12,X1),X0)) ) )
| ~ spl155_102
| ~ spl155_135 ),
inference(superposition,[],[f3477,f3837]) ).
thf(f3837,plain,
( ! [X0: product_prod_nat_nat > $o,X1: product_prod_nat_nat > $o] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X0)),vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X1)) )
| ( $true = vAPP(product_prod_nat_nat,$o,X0,vAPP(sTfun(product_prod_nat_nat,$o),product_prod_nat_nat,vAPP(sTfun(product_prod_nat_nat,$o),sTfun(sTfun(product_prod_nat_nat,$o),product_prod_nat_nat),sK12,X1),X0)) ) )
| ~ spl155_135 ),
inference(avatar_component_clause,[],[f3836]) ).
thf(f11344,plain,
( spl155_508
| ~ spl155_2
| ~ spl155_47 ),
inference(avatar_split_clause,[],[f3097,f3089,f2739,f11342]) ).
thf(f11342,plain,
( spl155_508
<=> ! [X0: product_prod_nat_nat,X1: list_P559422087at_nat] :
( ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,X0),vAPP(product_prod_nat_nat,list_P559422087at_nat,vAPP(list_P559422087at_nat,sTfun(product_prod_nat_nat,list_P559422087at_nat),sK31,X1),X0)) = X1 )
| ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(product_prod_nat_nat,product_prod_nat_nat,vAPP(list_P559422087at_nat,sTfun(product_prod_nat_nat,product_prod_nat_nat),sK29,X1),X0)),vAPP(product_prod_nat_nat,list_P559422087at_nat,vAPP(list_P559422087at_nat,sTfun(product_prod_nat_nat,list_P559422087at_nat),sK30,X1),X0)) = X1 )
| ( $false = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_508])]) ).
thf(f3089,plain,
( spl155_47
<=> ! [X0: product_prod_nat_nat,X1: list_P559422087at_nat] :
( ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(product_prod_nat_nat,product_prod_nat_nat,vAPP(list_P559422087at_nat,sTfun(product_prod_nat_nat,product_prod_nat_nat),sK29,X1),X0)),vAPP(product_prod_nat_nat,list_P559422087at_nat,vAPP(list_P559422087at_nat,sTfun(product_prod_nat_nat,list_P559422087at_nat),sK30,X1),X0)) = X1 )
| ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,X0),vAPP(product_prod_nat_nat,list_P559422087at_nat,vAPP(list_P559422087at_nat,sTfun(product_prod_nat_nat,list_P559422087at_nat),sK31,X1),X0)) = X1 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_47])]) ).
thf(f3097,plain,
( ! [X0: product_prod_nat_nat,X1: list_P559422087at_nat] :
( ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,X0),vAPP(product_prod_nat_nat,list_P559422087at_nat,vAPP(list_P559422087at_nat,sTfun(product_prod_nat_nat,list_P559422087at_nat),sK31,X1),X0)) = X1 )
| ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(product_prod_nat_nat,product_prod_nat_nat,vAPP(list_P559422087at_nat,sTfun(product_prod_nat_nat,product_prod_nat_nat),sK29,X1),X0)),vAPP(product_prod_nat_nat,list_P559422087at_nat,vAPP(list_P559422087at_nat,sTfun(product_prod_nat_nat,list_P559422087at_nat),sK30,X1),X0)) = X1 )
| ( $false = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X1)) ) )
| ~ spl155_2
| ~ spl155_47 ),
inference(trivial_inequality_removal,[],[f3096]) ).
thf(f3096,plain,
( ! [X0: product_prod_nat_nat,X1: list_P559422087at_nat] :
( ( $true != $true )
| ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,X0),vAPP(product_prod_nat_nat,list_P559422087at_nat,vAPP(list_P559422087at_nat,sTfun(product_prod_nat_nat,list_P559422087at_nat),sK31,X1),X0)) = X1 )
| ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(product_prod_nat_nat,product_prod_nat_nat,vAPP(list_P559422087at_nat,sTfun(product_prod_nat_nat,product_prod_nat_nat),sK29,X1),X0)),vAPP(product_prod_nat_nat,list_P559422087at_nat,vAPP(list_P559422087at_nat,sTfun(product_prod_nat_nat,list_P559422087at_nat),sK30,X1),X0)) = X1 )
| ( $false = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X1)) ) )
| ~ spl155_2
| ~ spl155_47 ),
inference(superposition,[],[f3090,f2740]) ).
thf(f3090,plain,
( ! [X0: product_prod_nat_nat,X1: list_P559422087at_nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X1)) )
| ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,X0),vAPP(product_prod_nat_nat,list_P559422087at_nat,vAPP(list_P559422087at_nat,sTfun(product_prod_nat_nat,list_P559422087at_nat),sK31,X1),X0)) = X1 )
| ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(product_prod_nat_nat,product_prod_nat_nat,vAPP(list_P559422087at_nat,sTfun(product_prod_nat_nat,product_prod_nat_nat),sK29,X1),X0)),vAPP(product_prod_nat_nat,list_P559422087at_nat,vAPP(list_P559422087at_nat,sTfun(product_prod_nat_nat,list_P559422087at_nat),sK30,X1),X0)) = X1 ) )
| ~ spl155_47 ),
inference(avatar_component_clause,[],[f3089]) ).
thf(f11340,plain,
( spl155_507
| ~ spl155_2
| ~ spl155_46 ),
inference(avatar_split_clause,[],[f3093,f3085,f2739,f11338]) ).
thf(f11338,plain,
( spl155_507
<=> ! [X0: nat,X1: list_nat] :
( ( vAPP(list_nat,list_nat,vAPP(nat,sTfun(list_nat,list_nat),cons_nat,X0),vAPP(nat,list_nat,vAPP(list_nat,sTfun(nat,list_nat),sK26,X1),X0)) = X1 )
| ( vAPP(list_nat,list_nat,vAPP(nat,sTfun(list_nat,list_nat),cons_nat,vAPP(nat,nat,vAPP(list_nat,sTfun(nat,nat),sK24,X1),X0)),vAPP(nat,list_nat,vAPP(list_nat,sTfun(nat,list_nat),sK25,X1),X0)) = X1 )
| ( $false = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(list_nat,set_nat,set_nat2,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_507])]) ).
thf(f3085,plain,
( spl155_46
<=> ! [X0: nat,X1: list_nat] :
( ( vAPP(list_nat,list_nat,vAPP(nat,sTfun(list_nat,list_nat),cons_nat,vAPP(nat,nat,vAPP(list_nat,sTfun(nat,nat),sK24,X1),X0)),vAPP(nat,list_nat,vAPP(list_nat,sTfun(nat,list_nat),sK25,X1),X0)) = X1 )
| ( vAPP(list_nat,list_nat,vAPP(nat,sTfun(list_nat,list_nat),cons_nat,X0),vAPP(nat,list_nat,vAPP(list_nat,sTfun(nat,list_nat),sK26,X1),X0)) = X1 )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(list_nat,set_nat,set_nat2,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_46])]) ).
thf(f3093,plain,
( ! [X0: nat,X1: list_nat] :
( ( vAPP(list_nat,list_nat,vAPP(nat,sTfun(list_nat,list_nat),cons_nat,X0),vAPP(nat,list_nat,vAPP(list_nat,sTfun(nat,list_nat),sK26,X1),X0)) = X1 )
| ( vAPP(list_nat,list_nat,vAPP(nat,sTfun(list_nat,list_nat),cons_nat,vAPP(nat,nat,vAPP(list_nat,sTfun(nat,nat),sK24,X1),X0)),vAPP(nat,list_nat,vAPP(list_nat,sTfun(nat,list_nat),sK25,X1),X0)) = X1 )
| ( $false = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(list_nat,set_nat,set_nat2,X1)) ) )
| ~ spl155_2
| ~ spl155_46 ),
inference(trivial_inequality_removal,[],[f3092]) ).
thf(f3092,plain,
( ! [X0: nat,X1: list_nat] :
( ( $true != $true )
| ( vAPP(list_nat,list_nat,vAPP(nat,sTfun(list_nat,list_nat),cons_nat,X0),vAPP(nat,list_nat,vAPP(list_nat,sTfun(nat,list_nat),sK26,X1),X0)) = X1 )
| ( vAPP(list_nat,list_nat,vAPP(nat,sTfun(list_nat,list_nat),cons_nat,vAPP(nat,nat,vAPP(list_nat,sTfun(nat,nat),sK24,X1),X0)),vAPP(nat,list_nat,vAPP(list_nat,sTfun(nat,list_nat),sK25,X1),X0)) = X1 )
| ( $false = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(list_nat,set_nat,set_nat2,X1)) ) )
| ~ spl155_2
| ~ spl155_46 ),
inference(superposition,[],[f3086,f2740]) ).
thf(f3086,plain,
( ! [X0: nat,X1: list_nat] :
( ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(list_nat,set_nat,set_nat2,X1)) )
| ( vAPP(list_nat,list_nat,vAPP(nat,sTfun(list_nat,list_nat),cons_nat,X0),vAPP(nat,list_nat,vAPP(list_nat,sTfun(nat,list_nat),sK26,X1),X0)) = X1 )
| ( vAPP(list_nat,list_nat,vAPP(nat,sTfun(list_nat,list_nat),cons_nat,vAPP(nat,nat,vAPP(list_nat,sTfun(nat,nat),sK24,X1),X0)),vAPP(nat,list_nat,vAPP(list_nat,sTfun(nat,list_nat),sK25,X1),X0)) = X1 ) )
| ~ spl155_46 ),
inference(avatar_component_clause,[],[f3085]) ).
thf(f11320,plain,
( spl155_506
| ~ spl155_247
| ~ spl155_260 ),
inference(avatar_split_clause,[],[f6288,f6266,f6142,f11318]) ).
thf(f11318,plain,
( spl155_506
<=> ! [X0: nat,X1: nat] :
( ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X1),vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),adjacent_nodes_a,c),X0)) )
| ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,vAPP(set_nat,nat,vAPP(nat,sTfun(set_nat,nat),sK23,X1),vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),adjacent_nodes_a,c),X0))),vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),adjacent_nodes_a,c),X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_506])]) ).
thf(f6142,plain,
( spl155_247
<=> ! [X0: nat] : ( $true = vAPP(set_nat,$o,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB))))),vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),adjacent_nodes_a,c),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_247])]) ).
thf(f6266,plain,
( spl155_260
<=> ! [X0: set_nat,X1: nat] :
( ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,vAPP(set_nat,nat,vAPP(nat,sTfun(set_nat,nat),sK23,X1),X0)),X0) )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X1),X0) )
| ( $true != vAPP(set_nat,$o,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB))))),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_260])]) ).
thf(f6288,plain,
( ! [X0: nat,X1: nat] :
( ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X1),vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),adjacent_nodes_a,c),X0)) )
| ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,vAPP(set_nat,nat,vAPP(nat,sTfun(set_nat,nat),sK23,X1),vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),adjacent_nodes_a,c),X0))),vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),adjacent_nodes_a,c),X0)) ) )
| ~ spl155_247
| ~ spl155_260 ),
inference(trivial_inequality_removal,[],[f6285]) ).
thf(f6285,plain,
( ! [X0: nat,X1: nat] :
( ( $true != $true )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X1),vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),adjacent_nodes_a,c),X0)) )
| ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,vAPP(set_nat,nat,vAPP(nat,sTfun(set_nat,nat),sK23,X1),vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),adjacent_nodes_a,c),X0))),vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),adjacent_nodes_a,c),X0)) ) )
| ~ spl155_247
| ~ spl155_260 ),
inference(superposition,[],[f6267,f6143]) ).
thf(f6143,plain,
( ! [X0: nat] : ( $true = vAPP(set_nat,$o,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB))))),vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),adjacent_nodes_a,c),X0)) )
| ~ spl155_247 ),
inference(avatar_component_clause,[],[f6142]) ).
thf(f6267,plain,
( ! [X0: set_nat,X1: nat] :
( ( $true != vAPP(set_nat,$o,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB))))),X0) )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X1),X0) )
| ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,vAPP(set_nat,nat,vAPP(nat,sTfun(set_nat,nat),sK23,X1),X0)),X0) ) )
| ~ spl155_260 ),
inference(avatar_component_clause,[],[f6266]) ).
thf(f11302,plain,
( spl155_505
| ~ spl155_247
| ~ spl155_259 ),
inference(avatar_split_clause,[],[f6276,f6262,f6142,f11300]) ).
thf(f11300,plain,
( spl155_505
<=> ! [X0: nat,X1: nat] :
( ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X1),vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),adjacent_nodes_a,c),X0)) )
| ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,vAPP(set_nat,nat,vAPP(nat,sTfun(set_nat,nat),sK22,X1),vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),adjacent_nodes_a,c),X0))),vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),adjacent_nodes_a,c),X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_505])]) ).
thf(f6262,plain,
( spl155_259
<=> ! [X0: set_nat,X1: nat] :
( ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,vAPP(set_nat,nat,vAPP(nat,sTfun(set_nat,nat),sK22,X1),X0)),X0) )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X1),X0) )
| ( $true != vAPP(set_nat,$o,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB))))),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_259])]) ).
thf(f6276,plain,
( ! [X0: nat,X1: nat] :
( ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X1),vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),adjacent_nodes_a,c),X0)) )
| ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,vAPP(set_nat,nat,vAPP(nat,sTfun(set_nat,nat),sK22,X1),vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),adjacent_nodes_a,c),X0))),vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),adjacent_nodes_a,c),X0)) ) )
| ~ spl155_247
| ~ spl155_259 ),
inference(trivial_inequality_removal,[],[f6273]) ).
thf(f6273,plain,
( ! [X0: nat,X1: nat] :
( ( $true != $true )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X1),vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),adjacent_nodes_a,c),X0)) )
| ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,vAPP(set_nat,nat,vAPP(nat,sTfun(set_nat,nat),sK22,X1),vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),adjacent_nodes_a,c),X0))),vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),adjacent_nodes_a,c),X0)) ) )
| ~ spl155_247
| ~ spl155_259 ),
inference(superposition,[],[f6263,f6143]) ).
thf(f6263,plain,
( ! [X0: set_nat,X1: nat] :
( ( $true != vAPP(set_nat,$o,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB))))),X0) )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X1),X0) )
| ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,vAPP(set_nat,nat,vAPP(nat,sTfun(set_nat,nat),sK22,X1),X0)),X0) ) )
| ~ spl155_259 ),
inference(avatar_component_clause,[],[f6262]) ).
thf(f11010,plain,
( spl155_504
| ~ spl155_105
| ~ spl155_133 ),
inference(avatar_split_clause,[],[f3830,f3814,f3488,f11007]) ).
thf(f11007,plain,
( spl155_504
<=> ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,c),s),t)) = vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK28,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,c)),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,c),s),t)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_504])]) ).
thf(f3814,plain,
( spl155_133
<=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,c),s),t))),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,c))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_133])]) ).
thf(f3830,plain,
( ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,c),s),t)) = vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK28,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,c)),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,c),s),t)))) )
| ~ spl155_105
| ~ spl155_133 ),
inference(trivial_inequality_removal,[],[f3821]) ).
thf(f3821,plain,
( ( $true != $true )
| ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,c),s),t)) = vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK28,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,c)),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,c),s),t)))) )
| ~ spl155_105
| ~ spl155_133 ),
inference(superposition,[],[f3489,f3816]) ).
thf(f3816,plain,
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,c),s),t))),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,c))) )
| ~ spl155_133 ),
inference(avatar_component_clause,[],[f3814]) ).
thf(f11005,plain,
( spl155_503
| ~ spl155_87
| ~ spl155_133 ),
inference(avatar_split_clause,[],[f3828,f3814,f3293,f11002]) ).
thf(f11002,plain,
( spl155_503
<=> ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,c),s),t)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,c))),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,c),s),t))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_503])]) ).
thf(f3828,plain,
( ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,c),s),t)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,c))),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,c),s),t))) )
| ~ spl155_87
| ~ spl155_133 ),
inference(trivial_inequality_removal,[],[f3823]) ).
thf(f3823,plain,
( ( $true != $true )
| ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,c),s),t)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,c))),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,c),s),t))) )
| ~ spl155_87
| ~ spl155_133 ),
inference(superposition,[],[f3294,f3816]) ).
thf(f11000,plain,
( spl155_502
| ~ spl155_86
| ~ spl155_133 ),
inference(avatar_split_clause,[],[f3827,f3814,f3289,f10997]) ).
thf(f10997,plain,
( spl155_502
<=> ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,c),s),t)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,c),s),t))),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,c))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_502])]) ).
thf(f3827,plain,
( ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,c),s),t)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,c),s),t))),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,c))) )
| ~ spl155_86
| ~ spl155_133 ),
inference(trivial_inequality_removal,[],[f3824]) ).
thf(f3824,plain,
( ( $true != $true )
| ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,c),s),t)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,c),s),t))),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,c))) )
| ~ spl155_86
| ~ spl155_133 ),
inference(superposition,[],[f3290,f3816]) ).
thf(f10995,plain,
( spl155_501
| ~ spl155_2
| ~ spl155_45 ),
inference(avatar_split_clause,[],[f3072,f3061,f2739,f10993]) ).
thf(f10993,plain,
( spl155_501
<=> ! [X2: nat,X0: nat > nat > $o,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK36,X0)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK37,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK38,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_501])]) ).
thf(f3061,plain,
( spl155_45
<=> ! [X2: nat,X0: nat > nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK36,X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK37,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK38,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_45])]) ).
thf(f3072,plain,
( ! [X2: nat,X0: nat > nat > $o,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK36,X0)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK37,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK38,X0)) ) )
| ~ spl155_2
| ~ spl155_45 ),
inference(trivial_inequality_removal,[],[f3071]) ).
thf(f3071,plain,
( ! [X2: nat,X0: nat > nat > $o,X1: nat] :
( ( $true != $true )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK36,X0)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK37,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK38,X0)) ) )
| ~ spl155_2
| ~ spl155_45 ),
inference(superposition,[],[f3062,f2740]) ).
thf(f3062,plain,
( ! [X2: nat,X0: nat > nat > $o,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK37,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK38,X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK36,X0)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2) ) )
| ~ spl155_45 ),
inference(avatar_component_clause,[],[f3061]) ).
thf(f10991,plain,
( spl155_500
| ~ spl155_354
| ~ spl155_462 ),
inference(avatar_split_clause,[],[f9993,f9843,f7593,f10989]) ).
thf(f10989,plain,
( spl155_500
<=> ! [X0: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),X0) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,X0),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p))),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_500])]) ).
thf(f9843,plain,
( spl155_462
<=> ! [X2: product_prod_nat_nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X2),X0) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X2),X1) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,X1),X0)),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_462])]) ).
thf(f9993,plain,
( ! [X0: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),X0) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,X0),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p))),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p)) ) )
| ~ spl155_354
| ~ spl155_462 ),
inference(trivial_inequality_removal,[],[f9985]) ).
thf(f9985,plain,
( ! [X0: set_Pr1986765409at_nat] :
( ( $true != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),X0) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,X0),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p))),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p)) ) )
| ~ spl155_354
| ~ spl155_462 ),
inference(superposition,[],[f9844,f7595]) ).
thf(f9844,plain,
( ! [X2: product_prod_nat_nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X2),X0) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X2),X1) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,X1),X0)),X0) ) )
| ~ spl155_462 ),
inference(avatar_component_clause,[],[f9843]) ).
thf(f10987,plain,
( spl155_499
| ~ spl155_2
| ~ spl155_44 ),
inference(avatar_split_clause,[],[f3066,f3057,f2739,f10985]) ).
thf(f10985,plain,
( spl155_499
<=> ! [X2: nat,X0: nat > nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK36,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,X0)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK37,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK38,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_499])]) ).
thf(f3057,plain,
( spl155_44
<=> ! [X2: nat,X0: nat > nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK36,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK37,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK38,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_44])]) ).
thf(f3066,plain,
( ! [X2: nat,X0: nat > nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK36,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,X0)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK37,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK38,X0)) ) )
| ~ spl155_2
| ~ spl155_44 ),
inference(trivial_inequality_removal,[],[f3065]) ).
thf(f3065,plain,
( ! [X2: nat,X0: nat > nat > $o,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK36,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,X0)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK37,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK38,X0)) ) )
| ~ spl155_2
| ~ spl155_44 ),
inference(superposition,[],[f3058,f2740]) ).
thf(f3058,plain,
( ! [X2: nat,X0: nat > nat > $o,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK37,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK38,X0)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK36,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,X0)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2) ) )
| ~ spl155_44 ),
inference(avatar_component_clause,[],[f3057]) ).
thf(f10961,plain,
( spl155_498
| ~ spl155_2
| ~ spl155_43 ),
inference(avatar_split_clause,[],[f3055,f3051,f2739,f10959]) ).
thf(f3051,plain,
( spl155_43
<=> ! [X4: product_prod_nat_nat,X0: product_prod_nat_nat > a,X3: nat,X2: list_P559422087at_nat,X1: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X4),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X4),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X2)) )
| ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,X0),X1),X2),X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_43])]) ).
thf(f3055,plain,
( ! [X2: list_P559422087at_nat,X3: nat,X0: product_prod_nat_nat > a,X1: nat,X4: product_prod_nat_nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X4),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X2)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X4),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) )
| ( $false = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,X0),X1),X2),X3) ) )
| ~ spl155_2
| ~ spl155_43 ),
inference(trivial_inequality_removal,[],[f3054]) ).
thf(f3054,plain,
( ! [X2: list_P559422087at_nat,X3: nat,X0: product_prod_nat_nat > a,X1: nat,X4: product_prod_nat_nat] :
( ( $true != $true )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X4),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X2)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X4),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) )
| ( $false = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,X0),X1),X2),X3) ) )
| ~ spl155_2
| ~ spl155_43 ),
inference(superposition,[],[f3052,f2740]) ).
thf(f3052,plain,
( ! [X2: list_P559422087at_nat,X3: nat,X0: product_prod_nat_nat > a,X1: nat,X4: product_prod_nat_nat] :
( ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,X0),X1),X2),X3) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X4),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X2)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X4),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) ) )
| ~ spl155_43 ),
inference(avatar_component_clause,[],[f3051]) ).
thf(f10947,plain,
( spl155_497
| ~ spl155_2
| ~ spl155_42 ),
inference(avatar_split_clause,[],[f3049,f3045,f2739,f10945]) ).
thf(f10945,plain,
( spl155_497
<=> ! [X2: nat,X0: list_P559422087at_nat,X1: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,nat)),sK63,X0),X1),X2))),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,$o)),sP6,X0),X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_497])]) ).
thf(f3045,plain,
( spl155_42
<=> ! [X2: list_P559422087at_nat,X0: nat,X1: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,nat)),sK63,X2),X1),X0))),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,$o)),sP6,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_42])]) ).
thf(f3049,plain,
( ! [X2: nat,X0: list_P559422087at_nat,X1: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,nat)),sK63,X0),X1),X2))),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,$o)),sP6,X0),X1),X2) ) )
| ~ spl155_2
| ~ spl155_42 ),
inference(trivial_inequality_removal,[],[f3048]) ).
thf(f3048,plain,
( ! [X2: nat,X0: list_P559422087at_nat,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,nat)),sK63,X0),X1),X2))),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,$o)),sP6,X0),X1),X2) ) )
| ~ spl155_2
| ~ spl155_42 ),
inference(superposition,[],[f3046,f2740]) ).
thf(f3046,plain,
( ! [X2: list_P559422087at_nat,X0: nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,$o)),sP6,X2),X1),X0) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,nat)),sK63,X2),X1),X0))),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) ) )
| ~ spl155_42 ),
inference(avatar_component_clause,[],[f3045]) ).
thf(f10905,plain,
( spl155_496
| ~ spl155_2
| ~ spl155_41 ),
inference(avatar_split_clause,[],[f3043,f3027,f2739,f10903]) ).
thf(f10903,plain,
( spl155_496
<=> ! [X0: product_prod_nat_nat,X1: list_P559422087at_nat] :
( ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,X0),vAPP(product_prod_nat_nat,list_P559422087at_nat,vAPP(list_P559422087at_nat,sTfun(product_prod_nat_nat,list_P559422087at_nat),sK31,X1),X0)) = X1 )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,vAPP(product_prod_nat_nat,list_P559422087at_nat,vAPP(list_P559422087at_nat,sTfun(product_prod_nat_nat,list_P559422087at_nat),sK30,X1),X0))) )
| ( $false = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_496])]) ).
thf(f3027,plain,
( spl155_41
<=> ! [X0: product_prod_nat_nat,X1: list_P559422087at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,vAPP(product_prod_nat_nat,list_P559422087at_nat,vAPP(list_P559422087at_nat,sTfun(product_prod_nat_nat,list_P559422087at_nat),sK30,X1),X0))) )
| ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,X0),vAPP(product_prod_nat_nat,list_P559422087at_nat,vAPP(list_P559422087at_nat,sTfun(product_prod_nat_nat,list_P559422087at_nat),sK31,X1),X0)) = X1 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_41])]) ).
thf(f3043,plain,
( ! [X0: product_prod_nat_nat,X1: list_P559422087at_nat] :
( ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,X0),vAPP(product_prod_nat_nat,list_P559422087at_nat,vAPP(list_P559422087at_nat,sTfun(product_prod_nat_nat,list_P559422087at_nat),sK31,X1),X0)) = X1 )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,vAPP(product_prod_nat_nat,list_P559422087at_nat,vAPP(list_P559422087at_nat,sTfun(product_prod_nat_nat,list_P559422087at_nat),sK30,X1),X0))) )
| ( $false = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X1)) ) )
| ~ spl155_2
| ~ spl155_41 ),
inference(trivial_inequality_removal,[],[f3042]) ).
thf(f3042,plain,
( ! [X0: product_prod_nat_nat,X1: list_P559422087at_nat] :
( ( $true != $true )
| ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,X0),vAPP(product_prod_nat_nat,list_P559422087at_nat,vAPP(list_P559422087at_nat,sTfun(product_prod_nat_nat,list_P559422087at_nat),sK31,X1),X0)) = X1 )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,vAPP(product_prod_nat_nat,list_P559422087at_nat,vAPP(list_P559422087at_nat,sTfun(product_prod_nat_nat,list_P559422087at_nat),sK30,X1),X0))) )
| ( $false = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X1)) ) )
| ~ spl155_2
| ~ spl155_41 ),
inference(superposition,[],[f3028,f2740]) ).
thf(f3028,plain,
( ! [X0: product_prod_nat_nat,X1: list_P559422087at_nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X1)) )
| ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,X0),vAPP(product_prod_nat_nat,list_P559422087at_nat,vAPP(list_P559422087at_nat,sTfun(product_prod_nat_nat,list_P559422087at_nat),sK31,X1),X0)) = X1 )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,vAPP(product_prod_nat_nat,list_P559422087at_nat,vAPP(list_P559422087at_nat,sTfun(product_prod_nat_nat,list_P559422087at_nat),sK30,X1),X0))) ) )
| ~ spl155_41 ),
inference(avatar_component_clause,[],[f3027]) ).
thf(f10901,plain,
( spl155_495
| ~ spl155_2
| ~ spl155_40 ),
inference(avatar_split_clause,[],[f3039,f3023,f2739,f10899]) ).
thf(f10899,plain,
( spl155_495
<=> ! [X0: nat,X1: list_nat] :
( ( vAPP(list_nat,list_nat,vAPP(nat,sTfun(list_nat,list_nat),cons_nat,X0),vAPP(nat,list_nat,vAPP(list_nat,sTfun(nat,list_nat),sK26,X1),X0)) = X1 )
| ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(list_nat,set_nat,set_nat2,vAPP(nat,list_nat,vAPP(list_nat,sTfun(nat,list_nat),sK25,X1),X0))) )
| ( $false = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(list_nat,set_nat,set_nat2,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_495])]) ).
thf(f3023,plain,
( spl155_40
<=> ! [X0: nat,X1: list_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(list_nat,set_nat,set_nat2,vAPP(nat,list_nat,vAPP(list_nat,sTfun(nat,list_nat),sK25,X1),X0))) )
| ( vAPP(list_nat,list_nat,vAPP(nat,sTfun(list_nat,list_nat),cons_nat,X0),vAPP(nat,list_nat,vAPP(list_nat,sTfun(nat,list_nat),sK26,X1),X0)) = X1 )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(list_nat,set_nat,set_nat2,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_40])]) ).
thf(f3039,plain,
( ! [X0: nat,X1: list_nat] :
( ( vAPP(list_nat,list_nat,vAPP(nat,sTfun(list_nat,list_nat),cons_nat,X0),vAPP(nat,list_nat,vAPP(list_nat,sTfun(nat,list_nat),sK26,X1),X0)) = X1 )
| ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(list_nat,set_nat,set_nat2,vAPP(nat,list_nat,vAPP(list_nat,sTfun(nat,list_nat),sK25,X1),X0))) )
| ( $false = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(list_nat,set_nat,set_nat2,X1)) ) )
| ~ spl155_2
| ~ spl155_40 ),
inference(trivial_inequality_removal,[],[f3038]) ).
thf(f3038,plain,
( ! [X0: nat,X1: list_nat] :
( ( $true != $true )
| ( vAPP(list_nat,list_nat,vAPP(nat,sTfun(list_nat,list_nat),cons_nat,X0),vAPP(nat,list_nat,vAPP(list_nat,sTfun(nat,list_nat),sK26,X1),X0)) = X1 )
| ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(list_nat,set_nat,set_nat2,vAPP(nat,list_nat,vAPP(list_nat,sTfun(nat,list_nat),sK25,X1),X0))) )
| ( $false = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(list_nat,set_nat,set_nat2,X1)) ) )
| ~ spl155_2
| ~ spl155_40 ),
inference(superposition,[],[f3024,f2740]) ).
thf(f3024,plain,
( ! [X0: nat,X1: list_nat] :
( ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(list_nat,set_nat,set_nat2,X1)) )
| ( vAPP(list_nat,list_nat,vAPP(nat,sTfun(list_nat,list_nat),cons_nat,X0),vAPP(nat,list_nat,vAPP(list_nat,sTfun(nat,list_nat),sK26,X1),X0)) = X1 )
| ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(list_nat,set_nat,set_nat2,vAPP(nat,list_nat,vAPP(list_nat,sTfun(nat,list_nat),sK25,X1),X0))) ) )
| ~ spl155_40 ),
inference(avatar_component_clause,[],[f3023]) ).
thf(f10827,plain,
( spl155_493
| ~ spl155_494
| ~ spl155_5
| ~ spl155_102
| ~ spl155_123 ),
inference(avatar_split_clause,[],[f3759,f3706,f3476,f2780,f10824,f10820]) ).
thf(f10820,plain,
( spl155_493
<=> ( vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c) = vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,c),s),t) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_493])]) ).
thf(f10824,plain,
( spl155_494
<=> ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,c),s),t)) = vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_494])]) ).
thf(f2780,plain,
( spl155_5
<=> ( vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_5])]) ).
thf(f3706,plain,
( spl155_123
<=> ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,c),s),t)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_123])]) ).
thf(f3759,plain,
( ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,c),s),t)) != vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) )
| ( vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c) = vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,c),s),t) )
| ~ spl155_5
| ~ spl155_102
| ~ spl155_123 ),
inference(trivial_inequality_removal,[],[f3758]) ).
thf(f3758,plain,
( ( $true != $true )
| ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,c),s),t)) != vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) )
| ( vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c) = vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,c),s),t) )
| ~ spl155_5
| ~ spl155_102
| ~ spl155_123 ),
inference(forward_demodulation,[],[f3756,f2782]) ).
thf(f2782,plain,
( ( vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) = $true )
| ~ spl155_5 ),
inference(avatar_component_clause,[],[f2780]) ).
thf(f3756,plain,
( ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,c),s),t)) != vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) )
| ( vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c) = vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,c),s),t) )
| ( vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) != $true )
| ~ spl155_102
| ~ spl155_123 ),
inference(trivial_inequality_removal,[],[f3749]) ).
thf(f3749,plain,
( ( $true != $true )
| ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,c),s),t)) != vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) )
| ( vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c) = vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,c),s),t) )
| ( vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) != $true )
| ~ spl155_102
| ~ spl155_123 ),
inference(superposition,[],[f3477,f3708]) ).
thf(f3708,plain,
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,c),s),t)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) )
| ~ spl155_123 ),
inference(avatar_component_clause,[],[f3706]) ).
thf(f10818,plain,
( spl155_492
| ~ spl155_2
| ~ spl155_39 ),
inference(avatar_split_clause,[],[f3020,f3015,f2739,f10816]) ).
thf(f10816,plain,
( spl155_492
<=> ! [X0: product_prod_nat_nat > a,X3: nat,X2: list_P559422087at_nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,X0),X1),X2),X3) )
| ( $false = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isShortestPath_a,X0),X1),X2),X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_492])]) ).
thf(f3015,plain,
( spl155_39
<=> ! [X0: product_prod_nat_nat > a,X3: nat,X2: list_P559422087at_nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,X0),X1),X2),X3) )
| ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isShortestPath_a,X0),X1),X2),X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_39])]) ).
thf(f3020,plain,
( ! [X2: list_P559422087at_nat,X3: nat,X0: product_prod_nat_nat > a,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,X0),X1),X2),X3) )
| ( $false = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isShortestPath_a,X0),X1),X2),X3) ) )
| ~ spl155_2
| ~ spl155_39 ),
inference(trivial_inequality_removal,[],[f3019]) ).
thf(f3019,plain,
( ! [X2: list_P559422087at_nat,X3: nat,X0: product_prod_nat_nat > a,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,X0),X1),X2),X3) )
| ( $false = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isShortestPath_a,X0),X1),X2),X3) ) )
| ~ spl155_2
| ~ spl155_39 ),
inference(superposition,[],[f3016,f2740]) ).
thf(f3016,plain,
( ! [X2: list_P559422087at_nat,X3: nat,X0: product_prod_nat_nat > a,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isShortestPath_a,X0),X1),X2),X3) )
| ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,X0),X1),X2),X3) ) )
| ~ spl155_39 ),
inference(avatar_component_clause,[],[f3015]) ).
thf(f10814,plain,
( spl155_491
| ~ spl155_96
| ~ spl155_102 ),
inference(avatar_split_clause,[],[f3542,f3476,f3420,f10812]) ).
thf(f10812,plain,
( spl155_491
<=> ! [X0: product_prod_nat_nat > a,X1: set_nat] :
( ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) != vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),incoming_a2,X0),X1)) )
| ( vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0) = vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),incoming_a2,X0),X1) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_491])]) ).
thf(f3420,plain,
( spl155_96
<=> ! [X0: product_prod_nat_nat > a,X1: set_nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),incoming_a2,X0),X1)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_96])]) ).
thf(f3542,plain,
( ! [X0: product_prod_nat_nat > a,X1: set_nat] :
( ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) != vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),incoming_a2,X0),X1)) )
| ( vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0) = vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),incoming_a2,X0),X1) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) ) )
| ~ spl155_96
| ~ spl155_102 ),
inference(trivial_inequality_removal,[],[f3533]) ).
thf(f3533,plain,
( ! [X0: product_prod_nat_nat > a,X1: set_nat] :
( ( $true != $true )
| ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) != vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),incoming_a2,X0),X1)) )
| ( vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0) = vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),incoming_a2,X0),X1) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) ) )
| ~ spl155_96
| ~ spl155_102 ),
inference(superposition,[],[f3477,f3421]) ).
thf(f3421,plain,
( ! [X0: product_prod_nat_nat > a,X1: set_nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),incoming_a2,X0),X1)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) )
| ~ spl155_96 ),
inference(avatar_component_clause,[],[f3420]) ).
thf(f10810,plain,
( spl155_490
| ~ spl155_97
| ~ spl155_102 ),
inference(avatar_split_clause,[],[f3541,f3476,f3424,f10808]) ).
thf(f10808,plain,
( spl155_490
<=> ! [X0: product_prod_nat_nat > a,X1: set_nat] :
( ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) != vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),outgoing_a2,X0),X1)) )
| ( vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0) = vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),outgoing_a2,X0),X1) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_490])]) ).
thf(f3424,plain,
( spl155_97
<=> ! [X0: product_prod_nat_nat > a,X1: set_nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),outgoing_a2,X0),X1)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_97])]) ).
thf(f3541,plain,
( ! [X0: product_prod_nat_nat > a,X1: set_nat] :
( ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) != vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),outgoing_a2,X0),X1)) )
| ( vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0) = vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),outgoing_a2,X0),X1) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) ) )
| ~ spl155_97
| ~ spl155_102 ),
inference(trivial_inequality_removal,[],[f3534]) ).
thf(f3534,plain,
( ! [X0: product_prod_nat_nat > a,X1: set_nat] :
( ( $true != $true )
| ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) != vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),outgoing_a2,X0),X1)) )
| ( vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0) = vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),outgoing_a2,X0),X1) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) ) )
| ~ spl155_97
| ~ spl155_102 ),
inference(superposition,[],[f3477,f3425]) ).
thf(f3425,plain,
( ! [X0: product_prod_nat_nat > a,X1: set_nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),outgoing_a2,X0),X1)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) )
| ~ spl155_97 ),
inference(avatar_component_clause,[],[f3424]) ).
thf(f10806,plain,
( spl155_489
| ~ spl155_349
| ~ spl155_478 ),
inference(avatar_split_clause,[],[f10710,f10491,f7504,f10804]) ).
thf(f10804,plain,
( spl155_489
<=> ! [X0: product_prod_nat_nat > $o] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X0)),edges)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p)) )
| ( $true = vAPP(product_prod_nat_nat,$o,X0,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_489])]) ).
thf(f10710,plain,
( ! [X0: product_prod_nat_nat > $o] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X0)),edges)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p)) )
| ( $true = vAPP(product_prod_nat_nat,$o,X0,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)) ) )
| ~ spl155_349
| ~ spl155_478 ),
inference(trivial_inequality_removal,[],[f10703]) ).
thf(f10703,plain,
( ! [X0: product_prod_nat_nat > $o] :
( ( $true != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X0)),edges)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p)) )
| ( $true = vAPP(product_prod_nat_nat,$o,X0,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)) ) )
| ~ spl155_349
| ~ spl155_478 ),
inference(superposition,[],[f7505,f10492]) ).
thf(f10802,plain,
( spl155_488
| ~ spl155_98
| ~ spl155_102 ),
inference(avatar_split_clause,[],[f3540,f3476,f3428,f10800]) ).
thf(f10800,plain,
( spl155_488
<=> ! [X0: product_prod_nat_nat > a,X1: nat] :
( ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) != vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),incoming_a,X0),X1)) )
| ( vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0) = vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),incoming_a,X0),X1) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_488])]) ).
thf(f3428,plain,
( spl155_98
<=> ! [X0: product_prod_nat_nat > a,X1: nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),incoming_a,X0),X1)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_98])]) ).
thf(f3540,plain,
( ! [X0: product_prod_nat_nat > a,X1: nat] :
( ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) != vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),incoming_a,X0),X1)) )
| ( vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0) = vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),incoming_a,X0),X1) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) ) )
| ~ spl155_98
| ~ spl155_102 ),
inference(trivial_inequality_removal,[],[f3535]) ).
thf(f3535,plain,
( ! [X0: product_prod_nat_nat > a,X1: nat] :
( ( $true != $true )
| ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) != vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),incoming_a,X0),X1)) )
| ( vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0) = vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),incoming_a,X0),X1) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) ) )
| ~ spl155_98
| ~ spl155_102 ),
inference(superposition,[],[f3477,f3429]) ).
thf(f3429,plain,
( ! [X0: product_prod_nat_nat > a,X1: nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),incoming_a,X0),X1)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) )
| ~ spl155_98 ),
inference(avatar_component_clause,[],[f3428]) ).
thf(f10798,plain,
( spl155_487
| ~ spl155_99
| ~ spl155_102 ),
inference(avatar_split_clause,[],[f3539,f3476,f3432,f10796]) ).
thf(f10796,plain,
( spl155_487
<=> ! [X0: product_prod_nat_nat > a,X1: nat] :
( ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) != vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),outgoing_a,X0),X1)) )
| ( vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0) = vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),outgoing_a,X0),X1) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_487])]) ).
thf(f3432,plain,
( spl155_99
<=> ! [X0: product_prod_nat_nat > a,X1: nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),outgoing_a,X0),X1)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_99])]) ).
thf(f3539,plain,
( ! [X0: product_prod_nat_nat > a,X1: nat] :
( ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) != vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),outgoing_a,X0),X1)) )
| ( vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0) = vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),outgoing_a,X0),X1) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) ) )
| ~ spl155_99
| ~ spl155_102 ),
inference(trivial_inequality_removal,[],[f3536]) ).
thf(f3536,plain,
( ! [X0: product_prod_nat_nat > a,X1: nat] :
( ( $true != $true )
| ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) != vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),outgoing_a,X0),X1)) )
| ( vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0) = vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),outgoing_a,X0),X1) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) ) )
| ~ spl155_99
| ~ spl155_102 ),
inference(superposition,[],[f3477,f3433]) ).
thf(f3433,plain,
( ! [X0: product_prod_nat_nat > a,X1: nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),outgoing_a,X0),X1)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) )
| ~ spl155_99 ),
inference(avatar_component_clause,[],[f3432]) ).
thf(f10768,plain,
( spl155_486
| ~ spl155_121
| ~ spl155_137 ),
inference(avatar_split_clause,[],[f3965,f3844,f3698,f10766]) ).
thf(f10766,plain,
( spl155_486
<=> ! [X2: nat,X0: nat > $o,X1: nat > $o] :
( ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X2),vAPP(sTfun(nat,$o),set_nat,collect_nat,X0)) )
| ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X2),vAPP(sTfun(nat,$o),set_nat,collect_nat,X1)) )
| ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(sTfun(nat,$o),sTfun(sTfun(nat,$o),nat),sK13,X1),X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_486])]) ).
thf(f3844,plain,
( spl155_137
<=> ! [X0: nat > $o,X1: nat > $o] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(sTfun(nat,$o),set_nat,collect_nat,X0)),vAPP(sTfun(nat,$o),set_nat,collect_nat,X1)) )
| ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(sTfun(nat,$o),sTfun(sTfun(nat,$o),nat),sK13,X1),X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_137])]) ).
thf(f3965,plain,
( ! [X2: nat,X0: nat > $o,X1: nat > $o] :
( ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X2),vAPP(sTfun(nat,$o),set_nat,collect_nat,X0)) )
| ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X2),vAPP(sTfun(nat,$o),set_nat,collect_nat,X1)) )
| ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(sTfun(nat,$o),sTfun(sTfun(nat,$o),nat),sK13,X1),X0)) ) )
| ~ spl155_121
| ~ spl155_137 ),
inference(trivial_inequality_removal,[],[f3894]) ).
thf(f3894,plain,
( ! [X2: nat,X0: nat > $o,X1: nat > $o] :
( ( $true != $true )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X2),vAPP(sTfun(nat,$o),set_nat,collect_nat,X0)) )
| ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X2),vAPP(sTfun(nat,$o),set_nat,collect_nat,X1)) )
| ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(sTfun(nat,$o),sTfun(sTfun(nat,$o),nat),sK13,X1),X0)) ) )
| ~ spl155_121
| ~ spl155_137 ),
inference(superposition,[],[f3699,f3845]) ).
thf(f3845,plain,
( ! [X0: nat > $o,X1: nat > $o] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(sTfun(nat,$o),set_nat,collect_nat,X0)),vAPP(sTfun(nat,$o),set_nat,collect_nat,X1)) )
| ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(sTfun(nat,$o),sTfun(sTfun(nat,$o),nat),sK13,X1),X0)) ) )
| ~ spl155_137 ),
inference(avatar_component_clause,[],[f3844]) ).
thf(f10764,plain,
( spl155_485
| ~ spl155_122
| ~ spl155_135 ),
inference(avatar_split_clause,[],[f3875,f3836,f3702,f10762]) ).
thf(f10762,plain,
( spl155_485
<=> ! [X2: product_prod_nat_nat,X0: product_prod_nat_nat > $o,X1: product_prod_nat_nat > $o] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X2),vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X0)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X2),vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X1)) )
| ( $true = vAPP(product_prod_nat_nat,$o,X0,vAPP(sTfun(product_prod_nat_nat,$o),product_prod_nat_nat,vAPP(sTfun(product_prod_nat_nat,$o),sTfun(sTfun(product_prod_nat_nat,$o),product_prod_nat_nat),sK12,X1),X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_485])]) ).
thf(f3875,plain,
( ! [X2: product_prod_nat_nat,X0: product_prod_nat_nat > $o,X1: product_prod_nat_nat > $o] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X2),vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X0)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X2),vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X1)) )
| ( $true = vAPP(product_prod_nat_nat,$o,X0,vAPP(sTfun(product_prod_nat_nat,$o),product_prod_nat_nat,vAPP(sTfun(product_prod_nat_nat,$o),sTfun(sTfun(product_prod_nat_nat,$o),product_prod_nat_nat),sK12,X1),X0)) ) )
| ~ spl155_122
| ~ spl155_135 ),
inference(trivial_inequality_removal,[],[f3863]) ).
thf(f3863,plain,
( ! [X2: product_prod_nat_nat,X0: product_prod_nat_nat > $o,X1: product_prod_nat_nat > $o] :
( ( $true != $true )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X2),vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X0)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X2),vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X1)) )
| ( $true = vAPP(product_prod_nat_nat,$o,X0,vAPP(sTfun(product_prod_nat_nat,$o),product_prod_nat_nat,vAPP(sTfun(product_prod_nat_nat,$o),sTfun(sTfun(product_prod_nat_nat,$o),product_prod_nat_nat),sK12,X1),X0)) ) )
| ~ spl155_122
| ~ spl155_135 ),
inference(superposition,[],[f3703,f3837]) ).
thf(f10720,plain,
( spl155_484
| ~ spl155_89
| ~ spl155_123 ),
inference(avatar_split_clause,[],[f3754,f3706,f3301,f10717]) ).
thf(f10717,plain,
( spl155_484
<=> ( vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,c),s),t) = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,c),s),t)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_484])]) ).
thf(f3754,plain,
( ( vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,c),s),t) = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,c),s),t)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) )
| ~ spl155_89
| ~ spl155_123 ),
inference(trivial_inequality_removal,[],[f3751]) ).
thf(f3751,plain,
( ( $true != $true )
| ( vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,c),s),t) = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,c),s),t)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) )
| ~ spl155_89
| ~ spl155_123 ),
inference(superposition,[],[f3302,f3708]) ).
thf(f10715,plain,
( spl155_483
| ~ spl155_88
| ~ spl155_123 ),
inference(avatar_split_clause,[],[f3753,f3706,f3297,f10712]) ).
thf(f10712,plain,
( spl155_483
<=> ( vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,c),s),t) = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,c),s),t)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_483])]) ).
thf(f3753,plain,
( ( vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,c),s),t) = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,c),s),t)) )
| ~ spl155_88
| ~ spl155_123 ),
inference(trivial_inequality_removal,[],[f3752]) ).
thf(f3752,plain,
( ( $true != $true )
| ( vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,c),s),t) = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,c),s),t)) )
| ~ spl155_88
| ~ spl155_123 ),
inference(superposition,[],[f3298,f3708]) ).
thf(f10527,plain,
( spl155_482
| ~ spl155_2
| ~ spl155_38 ),
inference(avatar_split_clause,[],[f3013,f3003,f2739,f10525]) ).
thf(f10525,plain,
( spl155_482
<=> ! [X2: nat,X0: nat,X1: list_P559422087at_nat] :
( ( X0 = X2 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,$o)),sP7,X1),X0),X2) )
| ( $false = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_482])]) ).
thf(f3003,plain,
( spl155_38
<=> ! [X2: nat,X0: nat,X1: list_P559422087at_nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,$o)),sP7,X1),X0),X2) )
| ( X0 = X2 )
| ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_38])]) ).
thf(f3013,plain,
( ! [X2: nat,X0: nat,X1: list_P559422087at_nat] :
( ( X0 = X2 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,$o)),sP7,X1),X0),X2) )
| ( $false = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2) ) )
| ~ spl155_2
| ~ spl155_38 ),
inference(trivial_inequality_removal,[],[f3012]) ).
thf(f3012,plain,
( ! [X2: nat,X0: nat,X1: list_P559422087at_nat] :
( ( $true != $true )
| ( X0 = X2 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,$o)),sP7,X1),X0),X2) )
| ( $false = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2) ) )
| ~ spl155_2
| ~ spl155_38 ),
inference(superposition,[],[f3004,f2740]) ).
thf(f3004,plain,
( ! [X2: nat,X0: nat,X1: list_P559422087at_nat] :
( ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2) )
| ( X0 = X2 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,$o)),sP7,X1),X0),X2) ) )
| ~ spl155_38 ),
inference(avatar_component_clause,[],[f3003]) ).
thf(f10523,plain,
( spl155_481
| ~ spl155_2
| ~ spl155_37 ),
inference(avatar_split_clause,[],[f3011,f2999,f2739,f10521]) ).
thf(f10521,plain,
( spl155_481
<=> ! [X2: nat,X0: nat,X1: list_P559422087at_nat] :
( ( nil_Pr1308055047at_nat = X1 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,$o)),sP7,X1),X0),X2) )
| ( $false = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_481])]) ).
thf(f2999,plain,
( spl155_37
<=> ! [X2: nat,X0: nat,X1: list_P559422087at_nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,$o)),sP7,X1),X0),X2) )
| ( nil_Pr1308055047at_nat = X1 )
| ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_37])]) ).
thf(f3011,plain,
( ! [X2: nat,X0: nat,X1: list_P559422087at_nat] :
( ( nil_Pr1308055047at_nat = X1 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,$o)),sP7,X1),X0),X2) )
| ( $false = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2) ) )
| ~ spl155_2
| ~ spl155_37 ),
inference(trivial_inequality_removal,[],[f3010]) ).
thf(f3010,plain,
( ! [X2: nat,X0: nat,X1: list_P559422087at_nat] :
( ( $true != $true )
| ( nil_Pr1308055047at_nat = X1 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,$o)),sP7,X1),X0),X2) )
| ( $false = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2) ) )
| ~ spl155_2
| ~ spl155_37 ),
inference(superposition,[],[f3000,f2740]) ).
thf(f3000,plain,
( ! [X2: nat,X0: nat,X1: list_P559422087at_nat] :
( ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2) )
| ( nil_Pr1308055047at_nat = X1 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,$o)),sP7,X1),X0),X2) ) )
| ~ spl155_37 ),
inference(avatar_component_clause,[],[f2999]) ).
thf(f10519,plain,
( spl155_480
| ~ spl155_2
| ~ spl155_35 ),
inference(avatar_split_clause,[],[f3009,f2991,f2739,f10517]) ).
thf(f10517,plain,
( spl155_480
<=> ! [X2: nat,X0: nat,X1: list_P559422087at_nat] :
( ( X0 = X2 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,$o)),sP6,X1),X0),X2) )
| ( $false = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_480])]) ).
thf(f2991,plain,
( spl155_35
<=> ! [X2: nat,X0: nat,X1: list_P559422087at_nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,$o)),sP6,X1),X0),X2) )
| ( X0 = X2 )
| ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_35])]) ).
thf(f3009,plain,
( ! [X2: nat,X0: nat,X1: list_P559422087at_nat] :
( ( X0 = X2 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,$o)),sP6,X1),X0),X2) )
| ( $false = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2) ) )
| ~ spl155_2
| ~ spl155_35 ),
inference(trivial_inequality_removal,[],[f3008]) ).
thf(f3008,plain,
( ! [X2: nat,X0: nat,X1: list_P559422087at_nat] :
( ( $true != $true )
| ( X0 = X2 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,$o)),sP6,X1),X0),X2) )
| ( $false = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2) ) )
| ~ spl155_2
| ~ spl155_35 ),
inference(superposition,[],[f2992,f2740]) ).
thf(f2992,plain,
( ! [X2: nat,X0: nat,X1: list_P559422087at_nat] :
( ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2) )
| ( X0 = X2 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,$o)),sP6,X1),X0),X2) ) )
| ~ spl155_35 ),
inference(avatar_component_clause,[],[f2991]) ).
thf(f10515,plain,
( spl155_479
| ~ spl155_2
| ~ spl155_34 ),
inference(avatar_split_clause,[],[f3007,f2987,f2739,f10513]) ).
thf(f10513,plain,
( spl155_479
<=> ! [X2: nat,X0: nat,X1: list_P559422087at_nat] :
( ( nil_Pr1308055047at_nat = X1 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,$o)),sP6,X1),X0),X2) )
| ( $false = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_479])]) ).
thf(f2987,plain,
( spl155_34
<=> ! [X2: nat,X0: nat,X1: list_P559422087at_nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,$o)),sP6,X1),X0),X2) )
| ( nil_Pr1308055047at_nat = X1 )
| ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_34])]) ).
thf(f3007,plain,
( ! [X2: nat,X0: nat,X1: list_P559422087at_nat] :
( ( nil_Pr1308055047at_nat = X1 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,$o)),sP6,X1),X0),X2) )
| ( $false = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2) ) )
| ~ spl155_2
| ~ spl155_34 ),
inference(trivial_inequality_removal,[],[f3006]) ).
thf(f3006,plain,
( ! [X2: nat,X0: nat,X1: list_P559422087at_nat] :
( ( $true != $true )
| ( nil_Pr1308055047at_nat = X1 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,$o)),sP6,X1),X0),X2) )
| ( $false = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2) ) )
| ~ spl155_2
| ~ spl155_34 ),
inference(superposition,[],[f2988,f2740]) ).
thf(f2988,plain,
( ! [X2: nat,X0: nat,X1: list_P559422087at_nat] :
( ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2) )
| ( nil_Pr1308055047at_nat = X1 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,$o)),sP6,X1),X0),X2) ) )
| ~ spl155_34 ),
inference(avatar_component_clause,[],[f2987]) ).
thf(f10493,plain,
( spl155_478
| ~ spl155_341
| ~ spl155_466 ),
inference(avatar_split_clause,[],[f10141,f10040,f7419,f10491]) ).
thf(f7419,plain,
( spl155_341
<=> ! [X0: product_prod_nat_nat,X1: product_prod_nat_nat > $o] :
( ( $false = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X1)) )
| ( $true = vAPP(product_prod_nat_nat,$o,X1,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_341])]) ).
thf(f10141,plain,
( ! [X0: product_prod_nat_nat > $o] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X0)),edges)),edges) )
| ( $true = vAPP(product_prod_nat_nat,$o,X0,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)) ) )
| ~ spl155_341
| ~ spl155_466 ),
inference(trivial_inequality_removal,[],[f10102]) ).
thf(f10102,plain,
( ! [X0: product_prod_nat_nat > $o] :
( ( $true = $false )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X0)),edges)),edges) )
| ( $true = vAPP(product_prod_nat_nat,$o,X0,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)) ) )
| ~ spl155_341
| ~ spl155_466 ),
inference(superposition,[],[f10041,f7420]) ).
thf(f7420,plain,
( ! [X0: product_prod_nat_nat,X1: product_prod_nat_nat > $o] :
( ( $false = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X1)) )
| ( $true = vAPP(product_prod_nat_nat,$o,X1,X0) ) )
| ~ spl155_341 ),
inference(avatar_component_clause,[],[f7419]) ).
thf(f10165,plain,
( spl155_477
| ~ spl155_245
| ~ spl155_260 ),
inference(avatar_split_clause,[],[f6290,f6266,f6127,f10163]) ).
thf(f10163,plain,
( spl155_477
<=> ! [X0: nat] :
( ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,c)) )
| ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,vAPP(set_nat,nat,vAPP(nat,sTfun(set_nat,nat),sK23,X0),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,c))),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,c)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_477])]) ).
thf(f6127,plain,
( spl155_245
<=> ( $true = vAPP(set_nat,$o,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB))))),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,c)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_245])]) ).
thf(f6290,plain,
( ! [X0: nat] :
( ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,c)) )
| ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,vAPP(set_nat,nat,vAPP(nat,sTfun(set_nat,nat),sK23,X0),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,c))),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,c)) ) )
| ~ spl155_245
| ~ spl155_260 ),
inference(trivial_inequality_removal,[],[f6283]) ).
thf(f6283,plain,
( ! [X0: nat] :
( ( $true != $true )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,c)) )
| ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,vAPP(set_nat,nat,vAPP(nat,sTfun(set_nat,nat),sK23,X0),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,c))),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,c)) ) )
| ~ spl155_245
| ~ spl155_260 ),
inference(superposition,[],[f6267,f6129]) ).
thf(f6129,plain,
( ( $true = vAPP(set_nat,$o,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB))))),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,c)) )
| ~ spl155_245 ),
inference(avatar_component_clause,[],[f6127]) ).
thf(f10161,plain,
( spl155_476
| ~ spl155_245
| ~ spl155_259 ),
inference(avatar_split_clause,[],[f6278,f6262,f6127,f10159]) ).
thf(f10159,plain,
( spl155_476
<=> ! [X0: nat] :
( ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,c)) )
| ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,vAPP(set_nat,nat,vAPP(nat,sTfun(set_nat,nat),sK22,X0),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,c))),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,c)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_476])]) ).
thf(f6278,plain,
( ! [X0: nat] :
( ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,c)) )
| ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,vAPP(set_nat,nat,vAPP(nat,sTfun(set_nat,nat),sK22,X0),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,c))),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,c)) ) )
| ~ spl155_245
| ~ spl155_259 ),
inference(trivial_inequality_removal,[],[f6271]) ).
thf(f6271,plain,
( ! [X0: nat] :
( ( $true != $true )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,c)) )
| ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,vAPP(set_nat,nat,vAPP(nat,sTfun(set_nat,nat),sK22,X0),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,c))),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,c)) ) )
| ~ spl155_245
| ~ spl155_259 ),
inference(superposition,[],[f6263,f6129]) ).
thf(f10157,plain,
( spl155_475
| ~ spl155_85
| ~ spl155_137 ),
inference(avatar_split_clause,[],[f3964,f3844,f3285,f10155]) ).
thf(f10155,plain,
( spl155_475
<=> ! [X0: nat > $o,X1: nat > $o] :
( ( vAPP(sTfun(nat,$o),set_nat,collect_nat,X0) = vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,vAPP(sTfun(nat,$o),set_nat,collect_nat,X0)),vAPP(sTfun(nat,$o),set_nat,collect_nat,X1)) )
| ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(sTfun(nat,$o),sTfun(sTfun(nat,$o),nat),sK13,X1),X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_475])]) ).
thf(f3964,plain,
( ! [X0: nat > $o,X1: nat > $o] :
( ( vAPP(sTfun(nat,$o),set_nat,collect_nat,X0) = vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,vAPP(sTfun(nat,$o),set_nat,collect_nat,X0)),vAPP(sTfun(nat,$o),set_nat,collect_nat,X1)) )
| ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(sTfun(nat,$o),sTfun(sTfun(nat,$o),nat),sK13,X1),X0)) ) )
| ~ spl155_85
| ~ spl155_137 ),
inference(trivial_inequality_removal,[],[f3895]) ).
thf(f3895,plain,
( ! [X0: nat > $o,X1: nat > $o] :
( ( $true != $true )
| ( vAPP(sTfun(nat,$o),set_nat,collect_nat,X0) = vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,vAPP(sTfun(nat,$o),set_nat,collect_nat,X0)),vAPP(sTfun(nat,$o),set_nat,collect_nat,X1)) )
| ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(sTfun(nat,$o),sTfun(sTfun(nat,$o),nat),sK13,X1),X0)) ) )
| ~ spl155_85
| ~ spl155_137 ),
inference(superposition,[],[f3286,f3845]) ).
thf(f10153,plain,
( spl155_474
| ~ spl155_84
| ~ spl155_137 ),
inference(avatar_split_clause,[],[f3963,f3844,f3281,f10151]) ).
thf(f10151,plain,
( spl155_474
<=> ! [X0: nat > $o,X1: nat > $o] :
( ( vAPP(sTfun(nat,$o),set_nat,collect_nat,X0) = vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,vAPP(sTfun(nat,$o),set_nat,collect_nat,X1)),vAPP(sTfun(nat,$o),set_nat,collect_nat,X0)) )
| ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(sTfun(nat,$o),sTfun(sTfun(nat,$o),nat),sK13,X1),X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_474])]) ).
thf(f3963,plain,
( ! [X0: nat > $o,X1: nat > $o] :
( ( vAPP(sTfun(nat,$o),set_nat,collect_nat,X0) = vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,vAPP(sTfun(nat,$o),set_nat,collect_nat,X1)),vAPP(sTfun(nat,$o),set_nat,collect_nat,X0)) )
| ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(sTfun(nat,$o),sTfun(sTfun(nat,$o),nat),sK13,X1),X0)) ) )
| ~ spl155_84
| ~ spl155_137 ),
inference(trivial_inequality_removal,[],[f3896]) ).
thf(f3896,plain,
( ! [X0: nat > $o,X1: nat > $o] :
( ( $true != $true )
| ( vAPP(sTfun(nat,$o),set_nat,collect_nat,X0) = vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,vAPP(sTfun(nat,$o),set_nat,collect_nat,X1)),vAPP(sTfun(nat,$o),set_nat,collect_nat,X0)) )
| ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(sTfun(nat,$o),sTfun(sTfun(nat,$o),nat),sK13,X1),X0)) ) )
| ~ spl155_84
| ~ spl155_137 ),
inference(superposition,[],[f3282,f3845]) ).
thf(f10149,plain,
( spl155_473
| ~ spl155_89
| ~ spl155_135 ),
inference(avatar_split_clause,[],[f3872,f3836,f3301,f10147]) ).
thf(f10147,plain,
( spl155_473
<=> ! [X0: product_prod_nat_nat > $o,X1: product_prod_nat_nat > $o] :
( ( vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X0) = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X0)),vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X1)) )
| ( $true = vAPP(product_prod_nat_nat,$o,X0,vAPP(sTfun(product_prod_nat_nat,$o),product_prod_nat_nat,vAPP(sTfun(product_prod_nat_nat,$o),sTfun(sTfun(product_prod_nat_nat,$o),product_prod_nat_nat),sK12,X1),X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_473])]) ).
thf(f3872,plain,
( ! [X0: product_prod_nat_nat > $o,X1: product_prod_nat_nat > $o] :
( ( vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X0) = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X0)),vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X1)) )
| ( $true = vAPP(product_prod_nat_nat,$o,X0,vAPP(sTfun(product_prod_nat_nat,$o),product_prod_nat_nat,vAPP(sTfun(product_prod_nat_nat,$o),sTfun(sTfun(product_prod_nat_nat,$o),product_prod_nat_nat),sK12,X1),X0)) ) )
| ~ spl155_89
| ~ spl155_135 ),
inference(trivial_inequality_removal,[],[f3866]) ).
thf(f3866,plain,
( ! [X0: product_prod_nat_nat > $o,X1: product_prod_nat_nat > $o] :
( ( $true != $true )
| ( vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X0) = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X0)),vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X1)) )
| ( $true = vAPP(product_prod_nat_nat,$o,X0,vAPP(sTfun(product_prod_nat_nat,$o),product_prod_nat_nat,vAPP(sTfun(product_prod_nat_nat,$o),sTfun(sTfun(product_prod_nat_nat,$o),product_prod_nat_nat),sK12,X1),X0)) ) )
| ~ spl155_89
| ~ spl155_135 ),
inference(superposition,[],[f3302,f3837]) ).
thf(f10145,plain,
( spl155_472
| ~ spl155_88
| ~ spl155_135 ),
inference(avatar_split_clause,[],[f3871,f3836,f3297,f10143]) ).
thf(f10143,plain,
( spl155_472
<=> ! [X0: product_prod_nat_nat > $o,X1: product_prod_nat_nat > $o] :
( ( vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X0) = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X1)),vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X0)) )
| ( $true = vAPP(product_prod_nat_nat,$o,X0,vAPP(sTfun(product_prod_nat_nat,$o),product_prod_nat_nat,vAPP(sTfun(product_prod_nat_nat,$o),sTfun(sTfun(product_prod_nat_nat,$o),product_prod_nat_nat),sK12,X1),X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_472])]) ).
thf(f3871,plain,
( ! [X0: product_prod_nat_nat > $o,X1: product_prod_nat_nat > $o] :
( ( vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X0) = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X1)),vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X0)) )
| ( $true = vAPP(product_prod_nat_nat,$o,X0,vAPP(sTfun(product_prod_nat_nat,$o),product_prod_nat_nat,vAPP(sTfun(product_prod_nat_nat,$o),sTfun(sTfun(product_prod_nat_nat,$o),product_prod_nat_nat),sK12,X1),X0)) ) )
| ~ spl155_88
| ~ spl155_135 ),
inference(trivial_inequality_removal,[],[f3867]) ).
thf(f3867,plain,
( ! [X0: product_prod_nat_nat > $o,X1: product_prod_nat_nat > $o] :
( ( $true != $true )
| ( vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X0) = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X1)),vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X0)) )
| ( $true = vAPP(product_prod_nat_nat,$o,X0,vAPP(sTfun(product_prod_nat_nat,$o),product_prod_nat_nat,vAPP(sTfun(product_prod_nat_nat,$o),sTfun(sTfun(product_prod_nat_nat,$o),product_prod_nat_nat),sK12,X1),X0)) ) )
| ~ spl155_88
| ~ spl155_135 ),
inference(superposition,[],[f3298,f3837]) ).
thf(f10071,plain,
( spl155_471
| ~ spl155_249
| ~ spl155_260 ),
inference(avatar_split_clause,[],[f6292,f6266,f6162,f10069]) ).
thf(f10069,plain,
( spl155_471
<=> ! [X2: nat,X0: set_nat,X1: nat] :
( ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X1),X0) )
| ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,vAPP(set_nat,nat,vAPP(nat,sTfun(set_nat,nat),sK23,X1),X0)),X0) )
| ( vAPP(set_nat,nat,finite_card_nat,vAPP(set_nat,set_nat,vAPP(nat,sTfun(set_nat,set_nat),sK10,X2),X0)) = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_471])]) ).
thf(f6162,plain,
( spl155_249
<=> ! [X0: set_nat,X1: nat] :
( ( vAPP(set_nat,nat,finite_card_nat,vAPP(set_nat,set_nat,vAPP(nat,sTfun(set_nat,set_nat),sK10,X1),X0)) = X1 )
| ( $true = vAPP(set_nat,$o,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB))))),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_249])]) ).
thf(f6292,plain,
( ! [X2: nat,X0: set_nat,X1: nat] :
( ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X1),X0) )
| ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,vAPP(set_nat,nat,vAPP(nat,sTfun(set_nat,nat),sK23,X1),X0)),X0) )
| ( vAPP(set_nat,nat,finite_card_nat,vAPP(set_nat,set_nat,vAPP(nat,sTfun(set_nat,set_nat),sK10,X2),X0)) = X2 ) )
| ~ spl155_249
| ~ spl155_260 ),
inference(trivial_inequality_removal,[],[f6281]) ).
thf(f6281,plain,
( ! [X2: nat,X0: set_nat,X1: nat] :
( ( $true != $true )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X1),X0) )
| ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,vAPP(set_nat,nat,vAPP(nat,sTfun(set_nat,nat),sK23,X1),X0)),X0) )
| ( vAPP(set_nat,nat,finite_card_nat,vAPP(set_nat,set_nat,vAPP(nat,sTfun(set_nat,set_nat),sK10,X2),X0)) = X2 ) )
| ~ spl155_249
| ~ spl155_260 ),
inference(superposition,[],[f6267,f6163]) ).
thf(f6163,plain,
( ! [X0: set_nat,X1: nat] :
( ( vAPP(set_nat,nat,finite_card_nat,vAPP(set_nat,set_nat,vAPP(nat,sTfun(set_nat,set_nat),sK10,X1),X0)) = X1 )
| ( $true = vAPP(set_nat,$o,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB))))),X0) ) )
| ~ spl155_249 ),
inference(avatar_component_clause,[],[f6162]) ).
thf(f10067,plain,
( spl155_470
| ~ spl155_249
| ~ spl155_259 ),
inference(avatar_split_clause,[],[f6280,f6262,f6162,f10065]) ).
thf(f10065,plain,
( spl155_470
<=> ! [X2: nat,X0: set_nat,X1: nat] :
( ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X1),X0) )
| ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,vAPP(set_nat,nat,vAPP(nat,sTfun(set_nat,nat),sK22,X1),X0)),X0) )
| ( vAPP(set_nat,nat,finite_card_nat,vAPP(set_nat,set_nat,vAPP(nat,sTfun(set_nat,set_nat),sK10,X2),X0)) = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_470])]) ).
thf(f6280,plain,
( ! [X2: nat,X0: set_nat,X1: nat] :
( ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X1),X0) )
| ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,vAPP(set_nat,nat,vAPP(nat,sTfun(set_nat,nat),sK22,X1),X0)),X0) )
| ( vAPP(set_nat,nat,finite_card_nat,vAPP(set_nat,set_nat,vAPP(nat,sTfun(set_nat,set_nat),sK10,X2),X0)) = X2 ) )
| ~ spl155_249
| ~ spl155_259 ),
inference(trivial_inequality_removal,[],[f6269]) ).
thf(f6269,plain,
( ! [X2: nat,X0: set_nat,X1: nat] :
( ( $true != $true )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X1),X0) )
| ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,vAPP(set_nat,nat,vAPP(nat,sTfun(set_nat,nat),sK22,X1),X0)),X0) )
| ( vAPP(set_nat,nat,finite_card_nat,vAPP(set_nat,set_nat,vAPP(nat,sTfun(set_nat,set_nat),sK10,X2),X0)) = X2 ) )
| ~ spl155_249
| ~ spl155_259 ),
inference(superposition,[],[f6263,f6163]) ).
thf(f10056,plain,
( spl155_469
| ~ spl155_122
| ~ spl155_123 ),
inference(avatar_split_clause,[],[f3757,f3706,f3702,f10054]) ).
thf(f10054,plain,
( spl155_469
<=> ! [X0: product_prod_nat_nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,c),s),t)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_469])]) ).
thf(f3757,plain,
( ! [X0: product_prod_nat_nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,c),s),t)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) ) )
| ~ spl155_122
| ~ spl155_123 ),
inference(trivial_inequality_removal,[],[f3748]) ).
thf(f3748,plain,
( ! [X0: product_prod_nat_nat] :
( ( $true != $true )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,c),s),t)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) ) )
| ~ spl155_122
| ~ spl155_123 ),
inference(superposition,[],[f3703,f3708]) ).
thf(f10050,plain,
( spl155_468
| ~ spl155_16 ),
inference(avatar_split_clause,[],[f2872,f2864,f10048]) ).
thf(f10048,plain,
( spl155_468
<=> ! [X0: set_nat,X1: set_nat] :
( ( X0 = X1 )
| ( vAPP(set_nat,sTfun(nat,$o),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat),X0) != vAPP(set_nat,sTfun(nat,$o),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_468])]) ).
thf(f2864,plain,
( spl155_16
<=> ! [X0: set_nat] : ( vAPP(sTfun(nat,$o),set_nat,collect_nat,vAPP(set_nat,sTfun(nat,$o),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat),X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_16])]) ).
thf(f2872,plain,
( ! [X0: set_nat,X1: set_nat] :
( ( X0 = X1 )
| ( vAPP(set_nat,sTfun(nat,$o),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat),X0) != vAPP(set_nat,sTfun(nat,$o),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat),X1) ) )
| ~ spl155_16 ),
inference(constrained_superposition,[],[f2865,f2865]) ).
thf(f2865,plain,
( ! [X0: set_nat] : ( vAPP(sTfun(nat,$o),set_nat,collect_nat,vAPP(set_nat,sTfun(nat,$o),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat),X0)) = X0 )
| ~ spl155_16 ),
inference(avatar_component_clause,[],[f2864]) ).
thf(f10046,plain,
( spl155_467
| ~ spl155_15 ),
inference(avatar_split_clause,[],[f2871,f2860,f10044]) ).
thf(f10044,plain,
( spl155_467
<=> ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( X0 = X1 )
| ( vAPP(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o),vAPP(sTfun(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o)),cCOMB,member701585322at_nat),X0) != vAPP(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o),vAPP(sTfun(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o)),cCOMB,member701585322at_nat),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_467])]) ).
thf(f2871,plain,
( ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( X0 = X1 )
| ( vAPP(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o),vAPP(sTfun(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o)),cCOMB,member701585322at_nat),X0) != vAPP(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o),vAPP(sTfun(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o)),cCOMB,member701585322at_nat),X1) ) )
| ~ spl155_15 ),
inference(constrained_superposition,[],[f2861,f2861]) ).
thf(f10042,plain,
( spl155_466
| ~ spl155_125
| ~ spl155_462 ),
inference(avatar_split_clause,[],[f10002,f9843,f3763,f10040]) ).
thf(f10002,plain,
( ! [X0: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),X0) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,X0),edges)),edges) ) )
| ~ spl155_125
| ~ spl155_462 ),
inference(trivial_inequality_removal,[],[f9976]) ).
thf(f9976,plain,
( ! [X0: set_Pr1986765409at_nat] :
( ( $true != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),X0) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,X0),edges)),edges) ) )
| ~ spl155_125
| ~ spl155_462 ),
inference(superposition,[],[f9844,f3765]) ).
thf(f9859,plain,
( spl155_465
| ~ spl155_248
| ~ spl155_260 ),
inference(avatar_split_clause,[],[f6291,f6266,f6148,f9857]) ).
thf(f9857,plain,
( spl155_465
<=> ! [X2: nat,X0: set_nat,X1: nat] :
( ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X1),X0) )
| ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,vAPP(set_nat,nat,vAPP(nat,sTfun(set_nat,nat),sK23,X1),X0)),X0) )
| ( $true = vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,X0),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_465])]) ).
thf(f6291,plain,
( ! [X2: nat,X0: set_nat,X1: nat] :
( ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X1),X0) )
| ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,vAPP(set_nat,nat,vAPP(nat,sTfun(set_nat,nat),sK23,X1),X0)),X0) )
| ( $true = vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,X0),X2) ) )
| ~ spl155_248
| ~ spl155_260 ),
inference(trivial_inequality_removal,[],[f6282]) ).
thf(f6282,plain,
( ! [X2: nat,X0: set_nat,X1: nat] :
( ( $true != $true )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X1),X0) )
| ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,vAPP(set_nat,nat,vAPP(nat,sTfun(set_nat,nat),sK23,X1),X0)),X0) )
| ( $true = vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,X0),X2) ) )
| ~ spl155_248
| ~ spl155_260 ),
inference(superposition,[],[f6267,f6149]) ).
thf(f9853,plain,
( spl155_464
| ~ spl155_248
| ~ spl155_259 ),
inference(avatar_split_clause,[],[f6279,f6262,f6148,f9851]) ).
thf(f9851,plain,
( spl155_464
<=> ! [X2: nat,X0: set_nat,X1: nat] :
( ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X1),X0) )
| ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,vAPP(set_nat,nat,vAPP(nat,sTfun(set_nat,nat),sK22,X1),X0)),X0) )
| ( $true = vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,X0),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_464])]) ).
thf(f6279,plain,
( ! [X2: nat,X0: set_nat,X1: nat] :
( ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X1),X0) )
| ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,vAPP(set_nat,nat,vAPP(nat,sTfun(set_nat,nat),sK22,X1),X0)),X0) )
| ( $true = vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,X0),X2) ) )
| ~ spl155_248
| ~ spl155_259 ),
inference(trivial_inequality_removal,[],[f6270]) ).
thf(f6270,plain,
( ! [X2: nat,X0: set_nat,X1: nat] :
( ( $true != $true )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X1),X0) )
| ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,vAPP(set_nat,nat,vAPP(nat,sTfun(set_nat,nat),sK22,X1),X0)),X0) )
| ( $true = vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,X0),X2) ) )
| ~ spl155_248
| ~ spl155_259 ),
inference(superposition,[],[f6263,f6149]) ).
thf(f9849,plain,
( spl155_463
| ~ spl155_90
| ~ spl155_135 ),
inference(avatar_split_clause,[],[f3873,f3836,f3367,f9847]) ).
thf(f9847,plain,
( spl155_463
<=> ! [X0: product_prod_nat_nat > $o,X1: product_prod_nat_nat > $o] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X0)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X1)) )
| ( $true = vAPP(product_prod_nat_nat,$o,X0,vAPP(sTfun(product_prod_nat_nat,$o),product_prod_nat_nat,vAPP(sTfun(product_prod_nat_nat,$o),sTfun(sTfun(product_prod_nat_nat,$o),product_prod_nat_nat),sK12,X1),X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_463])]) ).
thf(f3873,plain,
( ! [X0: product_prod_nat_nat > $o,X1: product_prod_nat_nat > $o] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X0)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X1)) )
| ( $true = vAPP(product_prod_nat_nat,$o,X0,vAPP(sTfun(product_prod_nat_nat,$o),product_prod_nat_nat,vAPP(sTfun(product_prod_nat_nat,$o),sTfun(sTfun(product_prod_nat_nat,$o),product_prod_nat_nat),sK12,X1),X0)) ) )
| ~ spl155_90
| ~ spl155_135 ),
inference(trivial_inequality_removal,[],[f3865]) ).
thf(f3865,plain,
( ! [X0: product_prod_nat_nat > $o,X1: product_prod_nat_nat > $o] :
( ( $true != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X0)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X1)) )
| ( $true = vAPP(product_prod_nat_nat,$o,X0,vAPP(sTfun(product_prod_nat_nat,$o),product_prod_nat_nat,vAPP(sTfun(product_prod_nat_nat,$o),sTfun(sTfun(product_prod_nat_nat,$o),product_prod_nat_nat),sK12,X1),X0)) ) )
| ~ spl155_90
| ~ spl155_135 ),
inference(superposition,[],[f3368,f3837]) ).
thf(f9845,plain,
( spl155_462
| ~ spl155_119
| ~ spl155_122 ),
inference(avatar_split_clause,[],[f3744,f3702,f3632,f9843]) ).
thf(f3744,plain,
( ! [X2: product_prod_nat_nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X2),X0) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X2),X1) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,X1),X0)),X0) ) )
| ~ spl155_119
| ~ spl155_122 ),
inference(trivial_inequality_removal,[],[f3729]) ).
thf(f3729,plain,
( ! [X2: product_prod_nat_nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true != $true )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X2),X0) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X2),X1) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,X1),X0)),X0) ) )
| ~ spl155_119
| ~ spl155_122 ),
inference(superposition,[],[f3703,f3633]) ).
thf(f9841,plain,
( spl155_461
| ~ spl155_117
| ~ spl155_121 ),
inference(avatar_split_clause,[],[f3722,f3698,f3624,f9839]) ).
thf(f9839,plain,
( spl155_461
<=> ! [X2: nat,X0: set_nat,X1: set_nat] :
( ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X2),X0) )
| ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X2),X1) )
| ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,vAPP(set_nat,nat,vAPP(set_nat,sTfun(set_nat,nat),sK15,X1),X0)),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_461])]) ).
thf(f3722,plain,
( ! [X2: nat,X0: set_nat,X1: set_nat] :
( ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X2),X0) )
| ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X2),X1) )
| ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,vAPP(set_nat,nat,vAPP(set_nat,sTfun(set_nat,nat),sK15,X1),X0)),X0) ) )
| ~ spl155_117
| ~ spl155_121 ),
inference(trivial_inequality_removal,[],[f3717]) ).
thf(f3717,plain,
( ! [X2: nat,X0: set_nat,X1: set_nat] :
( ( $true != $true )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X2),X0) )
| ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X2),X1) )
| ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,vAPP(set_nat,nat,vAPP(set_nat,sTfun(set_nat,nat),sK15,X1),X0)),X0) ) )
| ~ spl155_117
| ~ spl155_121 ),
inference(superposition,[],[f3699,f3625]) ).
thf(f9837,plain,
( spl155_460
| ~ spl155_2
| ~ spl155_33 ),
inference(avatar_split_clause,[],[f2985,f2977,f2739,f9835]) ).
thf(f2977,plain,
( spl155_33
<=> ! [X2: set_Pr1986765409at_nat,X0: product_prod_nat_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),X2)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),X2) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_33])]) ).
thf(f2985,plain,
( ! [X2: set_Pr1986765409at_nat,X0: product_prod_nat_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X2),X1)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),X2) )
| ( $false = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),X1) ) )
| ~ spl155_2
| ~ spl155_33 ),
inference(trivial_inequality_removal,[],[f2984]) ).
thf(f2984,plain,
( ! [X2: set_Pr1986765409at_nat,X0: product_prod_nat_nat,X1: set_Pr1986765409at_nat] :
( ( $true != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X2),X1)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),X2) )
| ( $false = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),X1) ) )
| ~ spl155_2
| ~ spl155_33 ),
inference(superposition,[],[f2978,f2740]) ).
thf(f2978,plain,
( ! [X2: set_Pr1986765409at_nat,X0: product_prod_nat_nat,X1: set_Pr1986765409at_nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),X2) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),X2)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),X1) ) )
| ~ spl155_33 ),
inference(avatar_component_clause,[],[f2977]) ).
thf(f9833,plain,
( spl155_459
| ~ spl155_2
| ~ spl155_32 ),
inference(avatar_split_clause,[],[f2982,f2973,f2739,f9831]) ).
thf(f9831,plain,
( spl155_459
<=> ! [X2: set_nat,X0: nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X2),X1)) )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),X2) )
| ( $false = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_459])]) ).
thf(f2973,plain,
( spl155_32
<=> ! [X2: set_nat,X0: nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),X2)) )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),X2) )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_32])]) ).
thf(f2982,plain,
( ! [X2: set_nat,X0: nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X2),X1)) )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),X2) )
| ( $false = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),X1) ) )
| ~ spl155_2
| ~ spl155_32 ),
inference(trivial_inequality_removal,[],[f2981]) ).
thf(f2981,plain,
( ! [X2: set_nat,X0: nat,X1: set_nat] :
( ( $true != $true )
| ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X2),X1)) )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),X2) )
| ( $false = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),X1) ) )
| ~ spl155_2
| ~ spl155_32 ),
inference(superposition,[],[f2974,f2740]) ).
thf(f2974,plain,
( ! [X2: set_nat,X0: nat,X1: set_nat] :
( ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),X2) )
| ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),X2)) )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),X1) ) )
| ~ spl155_32 ),
inference(avatar_component_clause,[],[f2973]) ).
thf(f9829,plain,
spl155_458,
inference(avatar_split_clause,[],[f2677,f9827]) ).
thf(f9827,plain,
( spl155_458
<=> ! [X2: set_nat,X0: nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),X2)) )
| ( $false = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),X2) )
| ( $false = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_458])]) ).
thf(f2677,plain,
! [X2: set_nat,X0: nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),X2)) )
| ( $false = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),X2) )
| ( $false = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),X1) ) ),
inference(binary_proxy_clausification,[],[f2673]) ).
thf(f2673,plain,
! [X2: set_nat,X0: nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),X2)) )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),X1)),vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),X2)) ) ),
inference(binary_proxy_clausification,[],[f1860]) ).
thf(f1860,plain,
! [X2: set_nat,X0: nat,X1: set_nat] : ( vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),X2)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),X1)),vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),X2)) ),
inference(cnf_transformation,[],[f735]) ).
thf(f735,plain,
! [X0: nat,X1: set_nat,X2: set_nat] : ( vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),X2)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),X1)),vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),X2)) ),
inference(fool_elimination,[],[f734]) ).
thf(f734,plain,
! [X0: nat,X1: set_nat,X2: set_nat] :
( ( vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),X2)) = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),X2) )
& vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),X1) ),
inference(rectify,[],[f151]) ).
thf(f151,axiom,
! [X9: nat,X2: set_nat,X3: set_nat] :
( ( vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X9),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X2),X3)) = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X9),X3) )
& vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X9),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_Int__iff) ).
thf(f9825,plain,
spl155_457,
inference(avatar_split_clause,[],[f2662,f9823]) ).
thf(f9823,plain,
( spl155_457
<=> ! [X2: set_Pr1986765409at_nat,X0: product_prod_nat_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),X2)) )
| ( $false = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),X2) )
| ( $false = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_457])]) ).
thf(f2662,plain,
! [X2: set_Pr1986765409at_nat,X0: product_prod_nat_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),X2)) )
| ( $false = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),X2) )
| ( $false = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),X1) ) ),
inference(binary_proxy_clausification,[],[f2658]) ).
thf(f2658,plain,
! [X2: set_Pr1986765409at_nat,X0: product_prod_nat_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),X2)) )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),X1)),vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),X2)) ) ),
inference(binary_proxy_clausification,[],[f1863]) ).
thf(f1863,plain,
! [X2: set_Pr1986765409at_nat,X0: product_prod_nat_nat,X1: set_Pr1986765409at_nat] : ( vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),X2)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),X1)),vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),X2)) ),
inference(cnf_transformation,[],[f741]) ).
thf(f741,plain,
! [X0: product_prod_nat_nat,X1: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat] : ( vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),X2)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),X1)),vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),X2)) ),
inference(fool_elimination,[],[f740]) ).
thf(f740,plain,
! [X0: product_prod_nat_nat,X1: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat] :
( ( vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),X2)) = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),X2) )
& vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),X1) ),
inference(rectify,[],[f152]) ).
thf(f152,axiom,
! [X9: product_prod_nat_nat,X2: set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat] :
( ( vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X9),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X2),X3)) = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X9),X3) )
& vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X9),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_Int__iff) ).
thf(f9799,plain,
( spl155_456
| ~ spl155_15
| ~ spl155_382 ),
inference(avatar_split_clause,[],[f8374,f8127,f2860,f9797]) ).
thf(f9797,plain,
( spl155_456
<=> ! [X0: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p))) )
| ( $false = vAPP(product_prod_nat_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o),vAPP(sTfun(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o)),cCOMB,member701585322at_nat),X0),vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_456])]) ).
thf(f8127,plain,
( spl155_382
<=> ! [X0: product_prod_nat_nat > $o] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X0)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p))) )
| ( $false = vAPP(product_prod_nat_nat,$o,X0,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_382])]) ).
thf(f8374,plain,
( ! [X0: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p))) )
| ( $false = vAPP(product_prod_nat_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o),vAPP(sTfun(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o)),cCOMB,member701585322at_nat),X0),vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)) ) )
| ~ spl155_15
| ~ spl155_382 ),
inference(superposition,[],[f8128,f2861]) ).
thf(f8128,plain,
( ! [X0: product_prod_nat_nat > $o] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X0)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p))) )
| ( $false = vAPP(product_prod_nat_nat,$o,X0,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)) ) )
| ~ spl155_382 ),
inference(avatar_component_clause,[],[f8127]) ).
thf(f9795,plain,
( spl155_455
| ~ spl155_244
| ~ spl155_260 ),
inference(avatar_split_clause,[],[f6289,f6266,f6123,f9793]) ).
thf(f9793,plain,
( spl155_455
<=> ! [X0: list_nat,X1: nat] :
( ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X1),vAPP(list_nat,set_nat,set_nat2,X0)) )
| ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,vAPP(set_nat,nat,vAPP(nat,sTfun(set_nat,nat),sK23,X1),vAPP(list_nat,set_nat,set_nat2,X0))),vAPP(list_nat,set_nat,set_nat2,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_455])]) ).
thf(f6289,plain,
( ! [X0: list_nat,X1: nat] :
( ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X1),vAPP(list_nat,set_nat,set_nat2,X0)) )
| ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,vAPP(set_nat,nat,vAPP(nat,sTfun(set_nat,nat),sK23,X1),vAPP(list_nat,set_nat,set_nat2,X0))),vAPP(list_nat,set_nat,set_nat2,X0)) ) )
| ~ spl155_244
| ~ spl155_260 ),
inference(trivial_inequality_removal,[],[f6284]) ).
thf(f6284,plain,
( ! [X0: list_nat,X1: nat] :
( ( $true != $true )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X1),vAPP(list_nat,set_nat,set_nat2,X0)) )
| ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,vAPP(set_nat,nat,vAPP(nat,sTfun(set_nat,nat),sK23,X1),vAPP(list_nat,set_nat,set_nat2,X0))),vAPP(list_nat,set_nat,set_nat2,X0)) ) )
| ~ spl155_244
| ~ spl155_260 ),
inference(superposition,[],[f6267,f6124]) ).
thf(f9791,plain,
( spl155_454
| ~ spl155_244
| ~ spl155_259 ),
inference(avatar_split_clause,[],[f6277,f6262,f6123,f9789]) ).
thf(f9789,plain,
( spl155_454
<=> ! [X0: list_nat,X1: nat] :
( ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X1),vAPP(list_nat,set_nat,set_nat2,X0)) )
| ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,vAPP(set_nat,nat,vAPP(nat,sTfun(set_nat,nat),sK22,X1),vAPP(list_nat,set_nat,set_nat2,X0))),vAPP(list_nat,set_nat,set_nat2,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_454])]) ).
thf(f6277,plain,
( ! [X0: list_nat,X1: nat] :
( ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X1),vAPP(list_nat,set_nat,set_nat2,X0)) )
| ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,vAPP(set_nat,nat,vAPP(nat,sTfun(set_nat,nat),sK22,X1),vAPP(list_nat,set_nat,set_nat2,X0))),vAPP(list_nat,set_nat,set_nat2,X0)) ) )
| ~ spl155_244
| ~ spl155_259 ),
inference(trivial_inequality_removal,[],[f6272]) ).
thf(f6272,plain,
( ! [X0: list_nat,X1: nat] :
( ( $true != $true )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X1),vAPP(list_nat,set_nat,set_nat2,X0)) )
| ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,vAPP(set_nat,nat,vAPP(nat,sTfun(set_nat,nat),sK22,X1),vAPP(list_nat,set_nat,set_nat2,X0))),vAPP(list_nat,set_nat,set_nat2,X0)) ) )
| ~ spl155_244
| ~ spl155_259 ),
inference(superposition,[],[f6263,f6124]) ).
thf(f9779,plain,
( spl155_453
| ~ spl155_104
| ~ spl155_133 ),
inference(avatar_split_clause,[],[f3829,f3814,f3484,f9776]) ).
thf(f9776,plain,
( spl155_453
<=> ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK28,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,c)),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,c),s),t)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_453])]) ).
thf(f3829,plain,
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK28,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,c)),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,c),s),t)))) )
| ~ spl155_104
| ~ spl155_133 ),
inference(trivial_inequality_removal,[],[f3822]) ).
thf(f3822,plain,
( ( $true != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK28,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,c)),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,c),s),t)))) )
| ~ spl155_104
| ~ spl155_133 ),
inference(superposition,[],[f3485,f3816]) ).
thf(f9644,plain,
( spl155_452
| ~ spl155_75
| ~ spl155_105 ),
inference(avatar_split_clause,[],[f3593,f3488,f3240,f9642]) ).
thf(f9642,plain,
( spl155_452
<=> ! [X0: set_Pr1986765409at_nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0)),X1) = vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK28,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0)),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_452])]) ).
thf(f3593,plain,
( ! [X0: set_Pr1986765409at_nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0)),X1) = vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK28,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0)),X1))) )
| ~ spl155_75
| ~ spl155_105 ),
inference(trivial_inequality_removal,[],[f3584]) ).
thf(f3584,plain,
( ! [X0: set_Pr1986765409at_nat,X1: nat] :
( ( $true != $true )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0)),X1) = vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK28,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0)),X1))) ) )
| ~ spl155_75
| ~ spl155_105 ),
inference(superposition,[],[f3489,f3241]) ).
thf(f9640,plain,
( spl155_451
| ~ spl155_74
| ~ spl155_105 ),
inference(avatar_split_clause,[],[f3592,f3488,f3236,f9638]) ).
thf(f9638,plain,
( spl155_451
<=> ! [X0: nat,X1: set_Pr1986765409at_nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)) = vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK28,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_451])]) ).
thf(f3592,plain,
( ! [X0: nat,X1: set_Pr1986765409at_nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)) = vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK28,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)))) )
| ~ spl155_74
| ~ spl155_105 ),
inference(trivial_inequality_removal,[],[f3585]) ).
thf(f3585,plain,
( ! [X0: nat,X1: set_Pr1986765409at_nat] :
( ( $true != $true )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)) = vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK28,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)))) ) )
| ~ spl155_74
| ~ spl155_105 ),
inference(superposition,[],[f3489,f3237]) ).
thf(f9634,plain,
( spl155_450
| ~ spl155_75
| ~ spl155_103 ),
inference(avatar_split_clause,[],[f3561,f3480,f3240,f9632]) ).
thf(f9632,plain,
( spl155_450
<=> ! [X0: set_nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,vAPP(set_nat,nat,finite_card_nat,X0)),X1) = vAPP(set_nat,nat,finite_card_nat,vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK27,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,vAPP(set_nat,nat,finite_card_nat,X0)),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_450])]) ).
thf(f3561,plain,
( ! [X0: set_nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,vAPP(set_nat,nat,finite_card_nat,X0)),X1) = vAPP(set_nat,nat,finite_card_nat,vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK27,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,vAPP(set_nat,nat,finite_card_nat,X0)),X1))) )
| ~ spl155_75
| ~ spl155_103 ),
inference(trivial_inequality_removal,[],[f3552]) ).
thf(f3552,plain,
( ! [X0: set_nat,X1: nat] :
( ( $true != $true )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,vAPP(set_nat,nat,finite_card_nat,X0)),X1) = vAPP(set_nat,nat,finite_card_nat,vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK27,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,vAPP(set_nat,nat,finite_card_nat,X0)),X1))) ) )
| ~ spl155_75
| ~ spl155_103 ),
inference(superposition,[],[f3481,f3241]) ).
thf(f9630,plain,
( spl155_449
| ~ spl155_74
| ~ spl155_103 ),
inference(avatar_split_clause,[],[f3560,f3480,f3236,f9628]) ).
thf(f9628,plain,
( spl155_449
<=> ! [X0: nat,X1: set_nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),vAPP(set_nat,nat,finite_card_nat,X1)) = vAPP(set_nat,nat,finite_card_nat,vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK27,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),vAPP(set_nat,nat,finite_card_nat,X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_449])]) ).
thf(f3560,plain,
( ! [X0: nat,X1: set_nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),vAPP(set_nat,nat,finite_card_nat,X1)) = vAPP(set_nat,nat,finite_card_nat,vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK27,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),vAPP(set_nat,nat,finite_card_nat,X1)))) )
| ~ spl155_74
| ~ spl155_103 ),
inference(trivial_inequality_removal,[],[f3553]) ).
thf(f3553,plain,
( ! [X0: nat,X1: set_nat] :
( ( $true != $true )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),vAPP(set_nat,nat,finite_card_nat,X1)) = vAPP(set_nat,nat,finite_card_nat,vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK27,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),vAPP(set_nat,nat,finite_card_nat,X1)))) ) )
| ~ spl155_74
| ~ spl155_103 ),
inference(superposition,[],[f3481,f3237]) ).
thf(f9626,plain,
( spl155_446
| spl155_447
| ~ spl155_448
| ~ spl155_44 ),
inference(avatar_split_clause,[],[f3069,f3057,f9623,f9619,f9616]) ).
thf(f9616,plain,
( spl155_446
<=> ! [X0: nat,X1: nat] : ( X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_446])]) ).
thf(f9619,plain,
( spl155_447
<=> ( vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK36,vEQ(nat)) = vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,vEQ(nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_447])]) ).
thf(f9623,plain,
( spl155_448
<=> ( vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK37,vEQ(nat)) = vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK38,vEQ(nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_448])]) ).
thf(f3069,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK37,vEQ(nat)) != vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK38,vEQ(nat)) )
| ( vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK36,vEQ(nat)) = vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,vEQ(nat)) )
| ( X0 = X1 ) )
| ~ spl155_44 ),
inference(equality_proxy_clausification,[],[f3068]) ).
thf(f3068,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK37,vEQ(nat)) != vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK38,vEQ(nat)) )
| ( vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK36,vEQ(nat)) = vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,vEQ(nat)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) ) )
| ~ spl155_44 ),
inference(equality_proxy_clausification,[],[f3067]) ).
thf(f3067,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK37,vEQ(nat)) != vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK38,vEQ(nat)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK36,vEQ(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,vEQ(nat))) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) ) )
| ~ spl155_44 ),
inference(equality_proxy_clausification,[],[f3064]) ).
thf(f3064,plain,
( ! [X0: nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK37,vEQ(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK38,vEQ(nat))) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK36,vEQ(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,vEQ(nat))) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) ) )
| ~ spl155_44 ),
inference(primitive_instantiation,[],[f3058]) ).
thf(f9586,plain,
( spl155_445
| ~ spl155_2
| spl155_31 ),
inference(avatar_split_clause,[],[f2971,f2966,f2739,f9583]) ).
thf(f2966,plain,
( spl155_31
<=> ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),edges),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_31])]) ).
thf(f2971,plain,
( ( $false = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),edges),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) )
| ~ spl155_2
| spl155_31 ),
inference(trivial_inequality_removal,[],[f2970]) ).
thf(f2970,plain,
( ( $true != $true )
| ( $false = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),edges),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) )
| ~ spl155_2
| spl155_31 ),
inference(superposition,[],[f2968,f2740]) ).
thf(f2968,plain,
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),edges),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) )
| spl155_31 ),
inference(avatar_component_clause,[],[f2966]) ).
thf(f9557,plain,
( spl155_444
| ~ spl155_15
| ~ spl155_344 ),
inference(avatar_split_clause,[],[f7507,f7452,f2860,f9555]) ).
thf(f9555,plain,
( spl155_444
<=> ! [X0: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),edges)) )
| ( $false = vAPP(product_prod_nat_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o),vAPP(sTfun(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o)),cCOMB,member701585322at_nat),X0),vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_444])]) ).
thf(f7452,plain,
( spl155_344
<=> ! [X0: product_prod_nat_nat > $o] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X0)),edges)) )
| ( $false = vAPP(product_prod_nat_nat,$o,X0,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_344])]) ).
thf(f7507,plain,
( ! [X0: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),edges)) )
| ( $false = vAPP(product_prod_nat_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o),vAPP(sTfun(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o)),cCOMB,member701585322at_nat),X0),vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)) ) )
| ~ spl155_15
| ~ spl155_344 ),
inference(superposition,[],[f7453,f2861]) ).
thf(f7453,plain,
( ! [X0: product_prod_nat_nat > $o] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X0)),edges)) )
| ( $false = vAPP(product_prod_nat_nat,$o,X0,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)) ) )
| ~ spl155_344 ),
inference(avatar_component_clause,[],[f7452]) ).
thf(f9526,plain,
( spl155_443
| ~ spl155_96
| ~ spl155_122 ),
inference(avatar_split_clause,[],[f3741,f3702,f3420,f9524]) ).
thf(f9524,plain,
( spl155_443
<=> ! [X2: product_prod_nat_nat,X0: product_prod_nat_nat > a,X1: set_nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X2),vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),incoming_a2,X0),X1)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X2),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_443])]) ).
thf(f3741,plain,
( ! [X2: product_prod_nat_nat,X0: product_prod_nat_nat > a,X1: set_nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X2),vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),incoming_a2,X0),X1)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X2),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) ) )
| ~ spl155_96
| ~ spl155_122 ),
inference(trivial_inequality_removal,[],[f3732]) ).
thf(f3732,plain,
( ! [X2: product_prod_nat_nat,X0: product_prod_nat_nat > a,X1: set_nat] :
( ( $true != $true )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X2),vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),incoming_a2,X0),X1)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X2),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) ) )
| ~ spl155_96
| ~ spl155_122 ),
inference(superposition,[],[f3703,f3421]) ).
thf(f9522,plain,
( spl155_442
| ~ spl155_97
| ~ spl155_122 ),
inference(avatar_split_clause,[],[f3740,f3702,f3424,f9520]) ).
thf(f9520,plain,
( spl155_442
<=> ! [X2: product_prod_nat_nat,X0: product_prod_nat_nat > a,X1: set_nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X2),vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),outgoing_a2,X0),X1)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X2),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_442])]) ).
thf(f3740,plain,
( ! [X2: product_prod_nat_nat,X0: product_prod_nat_nat > a,X1: set_nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X2),vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),outgoing_a2,X0),X1)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X2),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) ) )
| ~ spl155_97
| ~ spl155_122 ),
inference(trivial_inequality_removal,[],[f3733]) ).
thf(f3733,plain,
( ! [X2: product_prod_nat_nat,X0: product_prod_nat_nat > a,X1: set_nat] :
( ( $true != $true )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X2),vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),outgoing_a2,X0),X1)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X2),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) ) )
| ~ spl155_97
| ~ spl155_122 ),
inference(superposition,[],[f3703,f3425]) ).
thf(f9518,plain,
( spl155_441
| ~ spl155_98
| ~ spl155_122 ),
inference(avatar_split_clause,[],[f3739,f3702,f3428,f9516]) ).
thf(f9516,plain,
( spl155_441
<=> ! [X2: product_prod_nat_nat,X0: product_prod_nat_nat > a,X1: nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X2),vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),incoming_a,X0),X1)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X2),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_441])]) ).
thf(f3739,plain,
( ! [X2: product_prod_nat_nat,X0: product_prod_nat_nat > a,X1: nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X2),vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),incoming_a,X0),X1)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X2),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) ) )
| ~ spl155_98
| ~ spl155_122 ),
inference(trivial_inequality_removal,[],[f3734]) ).
thf(f3734,plain,
( ! [X2: product_prod_nat_nat,X0: product_prod_nat_nat > a,X1: nat] :
( ( $true != $true )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X2),vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),incoming_a,X0),X1)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X2),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) ) )
| ~ spl155_98
| ~ spl155_122 ),
inference(superposition,[],[f3703,f3429]) ).
thf(f9514,plain,
( spl155_440
| ~ spl155_99
| ~ spl155_122 ),
inference(avatar_split_clause,[],[f3738,f3702,f3432,f9512]) ).
thf(f9512,plain,
( spl155_440
<=> ! [X2: product_prod_nat_nat,X0: product_prod_nat_nat > a,X1: nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X2),vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),outgoing_a,X0),X1)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X2),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_440])]) ).
thf(f3738,plain,
( ! [X2: product_prod_nat_nat,X0: product_prod_nat_nat > a,X1: nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X2),vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),outgoing_a,X0),X1)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X2),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) ) )
| ~ spl155_99
| ~ spl155_122 ),
inference(trivial_inequality_removal,[],[f3735]) ).
thf(f3735,plain,
( ! [X2: product_prod_nat_nat,X0: product_prod_nat_nat > a,X1: nat] :
( ( $true != $true )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X2),vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),outgoing_a,X0),X1)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X2),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) ) )
| ~ spl155_99
| ~ spl155_122 ),
inference(superposition,[],[f3703,f3433]) ).
thf(f9510,plain,
( spl155_439
| ~ spl155_95
| ~ spl155_121 ),
inference(avatar_split_clause,[],[f3721,f3698,f3416,f9508]) ).
thf(f9508,plain,
( spl155_439
<=> ! [X2: nat,X0: product_prod_nat_nat > a,X1: nat] :
( ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X2),vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),adjacent_nodes_a,X0),X1)) )
| ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X2),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_439])]) ).
thf(f3416,plain,
( spl155_95
<=> ! [X0: product_prod_nat_nat > a,X1: nat] : ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),adjacent_nodes_a,X0),X1)),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_95])]) ).
thf(f3721,plain,
( ! [X2: nat,X0: product_prod_nat_nat > a,X1: nat] :
( ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X2),vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),adjacent_nodes_a,X0),X1)) )
| ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X2),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0)) ) )
| ~ spl155_95
| ~ spl155_121 ),
inference(trivial_inequality_removal,[],[f3718]) ).
thf(f3718,plain,
( ! [X2: nat,X0: product_prod_nat_nat > a,X1: nat] :
( ( $true != $true )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X2),vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),adjacent_nodes_a,X0),X1)) )
| ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X2),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0)) ) )
| ~ spl155_95
| ~ spl155_121 ),
inference(superposition,[],[f3699,f3417]) ).
thf(f3417,plain,
( ! [X0: product_prod_nat_nat > a,X1: nat] : ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),adjacent_nodes_a,X0),X1)),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0)) )
| ~ spl155_95 ),
inference(avatar_component_clause,[],[f3416]) ).
thf(f9506,plain,
( spl155_438
| ~ spl155_102
| ~ spl155_119 ),
inference(avatar_split_clause,[],[f3691,f3632,f3476,f9504]) ).
thf(f9504,plain,
( spl155_438
<=> ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0) != vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1) )
| ( X0 = X1 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X1) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,X1),X0)),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_438])]) ).
thf(f3691,plain,
( ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0) != vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1) )
| ( X0 = X1 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X1) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,X1),X0)),X0) ) )
| ~ spl155_102
| ~ spl155_119 ),
inference(trivial_inequality_removal,[],[f3671]) ).
thf(f3671,plain,
( ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true != $true )
| ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0) != vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1) )
| ( X0 = X1 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X1) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,X1),X0)),X0) ) )
| ~ spl155_102
| ~ spl155_119 ),
inference(superposition,[],[f3477,f3633]) ).
thf(f9277,plain,
( spl155_437
| ~ spl155_91
| ~ spl155_122 ),
inference(avatar_split_clause,[],[f3745,f3702,f3382,f9275]) ).
thf(f9275,plain,
( spl155_437
<=> ! [X2: product_prod_nat_nat,X0: nat,X1: set_Pr1986765409at_nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X2),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sK11,X0),X1)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X2),X1) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_437])]) ).
thf(f3745,plain,
( ! [X2: product_prod_nat_nat,X0: nat,X1: set_Pr1986765409at_nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X2),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sK11,X0),X1)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X2),X1) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X1) ) )
| ~ spl155_91
| ~ spl155_122 ),
inference(trivial_inequality_removal,[],[f3728]) ).
thf(f3728,plain,
( ! [X2: product_prod_nat_nat,X0: nat,X1: set_Pr1986765409at_nat] :
( ( $true != $true )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X2),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sK11,X0),X1)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X2),X1) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X1) ) )
| ~ spl155_91
| ~ spl155_122 ),
inference(superposition,[],[f3703,f3383]) ).
thf(f9273,plain,
( spl155_436
| ~ spl155_89
| ~ spl155_99 ),
inference(avatar_split_clause,[],[f3469,f3432,f3301,f9271]) ).
thf(f9271,plain,
( spl155_436
<=> ! [X0: product_prod_nat_nat > a,X1: nat] : ( vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),outgoing_a,X0),X1) = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),outgoing_a,X0),X1)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_436])]) ).
thf(f3469,plain,
( ! [X0: product_prod_nat_nat > a,X1: nat] : ( vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),outgoing_a,X0),X1) = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),outgoing_a,X0),X1)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) )
| ~ spl155_89
| ~ spl155_99 ),
inference(trivial_inequality_removal,[],[f3466]) ).
thf(f3466,plain,
( ! [X0: product_prod_nat_nat > a,X1: nat] :
( ( $true != $true )
| ( vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),outgoing_a,X0),X1) = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),outgoing_a,X0),X1)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) ) )
| ~ spl155_89
| ~ spl155_99 ),
inference(superposition,[],[f3302,f3433]) ).
thf(f9269,plain,
( spl155_435
| ~ spl155_88
| ~ spl155_99 ),
inference(avatar_split_clause,[],[f3468,f3432,f3297,f9267]) ).
thf(f9267,plain,
( spl155_435
<=> ! [X0: product_prod_nat_nat > a,X1: nat] : ( vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),outgoing_a,X0),X1) = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)),vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),outgoing_a,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_435])]) ).
thf(f3468,plain,
( ! [X0: product_prod_nat_nat > a,X1: nat] : ( vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),outgoing_a,X0),X1) = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)),vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),outgoing_a,X0),X1)) )
| ~ spl155_88
| ~ spl155_99 ),
inference(trivial_inequality_removal,[],[f3467]) ).
thf(f3467,plain,
( ! [X0: product_prod_nat_nat > a,X1: nat] :
( ( $true != $true )
| ( vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),outgoing_a,X0),X1) = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)),vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),outgoing_a,X0),X1)) ) )
| ~ spl155_88
| ~ spl155_99 ),
inference(superposition,[],[f3298,f3433]) ).
thf(f9265,plain,
( spl155_434
| ~ spl155_89
| ~ spl155_98 ),
inference(avatar_split_clause,[],[f3463,f3428,f3301,f9263]) ).
thf(f9263,plain,
( spl155_434
<=> ! [X0: product_prod_nat_nat > a,X1: nat] : ( vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),incoming_a,X0),X1) = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),incoming_a,X0),X1)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_434])]) ).
thf(f3463,plain,
( ! [X0: product_prod_nat_nat > a,X1: nat] : ( vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),incoming_a,X0),X1) = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),incoming_a,X0),X1)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) )
| ~ spl155_89
| ~ spl155_98 ),
inference(trivial_inequality_removal,[],[f3460]) ).
thf(f3460,plain,
( ! [X0: product_prod_nat_nat > a,X1: nat] :
( ( $true != $true )
| ( vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),incoming_a,X0),X1) = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),incoming_a,X0),X1)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) ) )
| ~ spl155_89
| ~ spl155_98 ),
inference(superposition,[],[f3302,f3429]) ).
thf(f9261,plain,
( spl155_433
| ~ spl155_88
| ~ spl155_98 ),
inference(avatar_split_clause,[],[f3462,f3428,f3297,f9259]) ).
thf(f9259,plain,
( spl155_433
<=> ! [X0: product_prod_nat_nat > a,X1: nat] : ( vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),incoming_a,X0),X1) = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)),vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),incoming_a,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_433])]) ).
thf(f3462,plain,
( ! [X0: product_prod_nat_nat > a,X1: nat] : ( vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),incoming_a,X0),X1) = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)),vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),incoming_a,X0),X1)) )
| ~ spl155_88
| ~ spl155_98 ),
inference(trivial_inequality_removal,[],[f3461]) ).
thf(f3461,plain,
( ! [X0: product_prod_nat_nat > a,X1: nat] :
( ( $true != $true )
| ( vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),incoming_a,X0),X1) = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)),vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),incoming_a,X0),X1)) ) )
| ~ spl155_88
| ~ spl155_98 ),
inference(superposition,[],[f3298,f3429]) ).
thf(f9257,plain,
( spl155_432
| ~ spl155_89
| ~ spl155_97 ),
inference(avatar_split_clause,[],[f3457,f3424,f3301,f9255]) ).
thf(f9255,plain,
( spl155_432
<=> ! [X0: product_prod_nat_nat > a,X1: set_nat] : ( vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),outgoing_a2,X0),X1) = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),outgoing_a2,X0),X1)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_432])]) ).
thf(f3457,plain,
( ! [X0: product_prod_nat_nat > a,X1: set_nat] : ( vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),outgoing_a2,X0),X1) = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),outgoing_a2,X0),X1)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) )
| ~ spl155_89
| ~ spl155_97 ),
inference(trivial_inequality_removal,[],[f3454]) ).
thf(f3454,plain,
( ! [X0: product_prod_nat_nat > a,X1: set_nat] :
( ( $true != $true )
| ( vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),outgoing_a2,X0),X1) = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),outgoing_a2,X0),X1)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) ) )
| ~ spl155_89
| ~ spl155_97 ),
inference(superposition,[],[f3302,f3425]) ).
thf(f9253,plain,
( spl155_431
| ~ spl155_181
| ~ spl155_382 ),
inference(avatar_split_clause,[],[f8381,f8127,f4909,f9251]) ).
thf(f9251,plain,
( spl155_431
<=> ! [X0: product_prod_nat_nat > $o] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X0)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p))),edges)) )
| ( $false = vAPP(product_prod_nat_nat,$o,X0,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_431])]) ).
thf(f8381,plain,
( ! [X0: product_prod_nat_nat > $o] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X0)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p))),edges)) )
| ( $false = vAPP(product_prod_nat_nat,$o,X0,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)) ) )
| ~ spl155_181
| ~ spl155_382 ),
inference(trivial_inequality_removal,[],[f8378]) ).
thf(f8378,plain,
( ! [X0: product_prod_nat_nat > $o] :
( ( $true != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X0)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p))),edges)) )
| ( $false = vAPP(product_prod_nat_nat,$o,X0,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)) ) )
| ~ spl155_181
| ~ spl155_382 ),
inference(superposition,[],[f4910,f8128]) ).
thf(f9249,plain,
( spl155_430
| ~ spl155_88
| ~ spl155_97 ),
inference(avatar_split_clause,[],[f3456,f3424,f3297,f9247]) ).
thf(f9247,plain,
( spl155_430
<=> ! [X0: product_prod_nat_nat > a,X1: set_nat] : ( vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),outgoing_a2,X0),X1) = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)),vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),outgoing_a2,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_430])]) ).
thf(f3456,plain,
( ! [X0: product_prod_nat_nat > a,X1: set_nat] : ( vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),outgoing_a2,X0),X1) = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)),vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),outgoing_a2,X0),X1)) )
| ~ spl155_88
| ~ spl155_97 ),
inference(trivial_inequality_removal,[],[f3455]) ).
thf(f3455,plain,
( ! [X0: product_prod_nat_nat > a,X1: set_nat] :
( ( $true != $true )
| ( vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),outgoing_a2,X0),X1) = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)),vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),outgoing_a2,X0),X1)) ) )
| ~ spl155_88
| ~ spl155_97 ),
inference(superposition,[],[f3298,f3425]) ).
thf(f9245,plain,
( spl155_429
| ~ spl155_89
| ~ spl155_96 ),
inference(avatar_split_clause,[],[f3451,f3420,f3301,f9243]) ).
thf(f9243,plain,
( spl155_429
<=> ! [X0: product_prod_nat_nat > a,X1: set_nat] : ( vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),incoming_a2,X0),X1) = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),incoming_a2,X0),X1)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_429])]) ).
thf(f3451,plain,
( ! [X0: product_prod_nat_nat > a,X1: set_nat] : ( vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),incoming_a2,X0),X1) = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),incoming_a2,X0),X1)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) )
| ~ spl155_89
| ~ spl155_96 ),
inference(trivial_inequality_removal,[],[f3448]) ).
thf(f3448,plain,
( ! [X0: product_prod_nat_nat > a,X1: set_nat] :
( ( $true != $true )
| ( vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),incoming_a2,X0),X1) = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),incoming_a2,X0),X1)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) ) )
| ~ spl155_89
| ~ spl155_96 ),
inference(superposition,[],[f3302,f3421]) ).
thf(f9241,plain,
( spl155_428
| ~ spl155_88
| ~ spl155_96 ),
inference(avatar_split_clause,[],[f3450,f3420,f3297,f9239]) ).
thf(f9239,plain,
( spl155_428
<=> ! [X0: product_prod_nat_nat > a,X1: set_nat] : ( vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),incoming_a2,X0),X1) = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)),vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),incoming_a2,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_428])]) ).
thf(f3450,plain,
( ! [X0: product_prod_nat_nat > a,X1: set_nat] : ( vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),incoming_a2,X0),X1) = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)),vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),incoming_a2,X0),X1)) )
| ~ spl155_88
| ~ spl155_96 ),
inference(trivial_inequality_removal,[],[f3449]) ).
thf(f3449,plain,
( ! [X0: product_prod_nat_nat > a,X1: set_nat] :
( ( $true != $true )
| ( vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),incoming_a2,X0),X1) = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)),vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),incoming_a2,X0),X1)) ) )
| ~ spl155_88
| ~ spl155_96 ),
inference(superposition,[],[f3298,f3421]) ).
thf(f9237,plain,
( spl155_427
| ~ spl155_85
| ~ spl155_95 ),
inference(avatar_split_clause,[],[f3446,f3416,f3285,f9235]) ).
thf(f9235,plain,
( spl155_427
<=> ! [X0: product_prod_nat_nat > a,X1: nat] : ( vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),adjacent_nodes_a,X0),X1) = vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),adjacent_nodes_a,X0),X1)),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_427])]) ).
thf(f3446,plain,
( ! [X0: product_prod_nat_nat > a,X1: nat] : ( vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),adjacent_nodes_a,X0),X1) = vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),adjacent_nodes_a,X0),X1)),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0)) )
| ~ spl155_85
| ~ spl155_95 ),
inference(trivial_inequality_removal,[],[f3443]) ).
thf(f3443,plain,
( ! [X0: product_prod_nat_nat > a,X1: nat] :
( ( $true != $true )
| ( vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),adjacent_nodes_a,X0),X1) = vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),adjacent_nodes_a,X0),X1)),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0)) ) )
| ~ spl155_85
| ~ spl155_95 ),
inference(superposition,[],[f3286,f3417]) ).
thf(f9233,plain,
( spl155_426
| ~ spl155_84
| ~ spl155_95 ),
inference(avatar_split_clause,[],[f3445,f3416,f3281,f9231]) ).
thf(f9231,plain,
( spl155_426
<=> ! [X0: product_prod_nat_nat > a,X1: nat] : ( vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),adjacent_nodes_a,X0),X1) = vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0)),vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),adjacent_nodes_a,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_426])]) ).
thf(f3445,plain,
( ! [X0: product_prod_nat_nat > a,X1: nat] : ( vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),adjacent_nodes_a,X0),X1) = vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0)),vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),adjacent_nodes_a,X0),X1)) )
| ~ spl155_84
| ~ spl155_95 ),
inference(trivial_inequality_removal,[],[f3444]) ).
thf(f3444,plain,
( ! [X0: product_prod_nat_nat > a,X1: nat] :
( ( $true != $true )
| ( vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),adjacent_nodes_a,X0),X1) = vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0)),vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),adjacent_nodes_a,X0),X1)) ) )
| ~ spl155_84
| ~ spl155_95 ),
inference(superposition,[],[f3282,f3417]) ).
thf(f9229,plain,
( spl155_425
| ~ spl155_2
| ~ spl155_29 ),
inference(avatar_split_clause,[],[f2964,f2950,f2739,f9227]) ).
thf(f9227,plain,
( spl155_425
<=> ! [X0: set_Pr1986765409at_nat,X1: set_se1612935105at_nat] :
( ( $true = vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK21,X0),X1)),X1) )
| ( $true != vAPP(set_se1612935105at_nat,$o,finite1457549322at_nat,X1) )
| ( $false = vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_425])]) ).
thf(f2950,plain,
( spl155_29
<=> ! [X0: set_se1612935105at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK21,X1),X0)),X0) )
| ( $true != vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X1),X0) )
| ( $true != vAPP(set_se1612935105at_nat,$o,finite1457549322at_nat,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_29])]) ).
thf(f2964,plain,
( ! [X0: set_Pr1986765409at_nat,X1: set_se1612935105at_nat] :
( ( $true = vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK21,X0),X1)),X1) )
| ( $true != vAPP(set_se1612935105at_nat,$o,finite1457549322at_nat,X1) )
| ( $false = vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X0),X1) ) )
| ~ spl155_2
| ~ spl155_29 ),
inference(trivial_inequality_removal,[],[f2963]) ).
thf(f2963,plain,
( ! [X0: set_Pr1986765409at_nat,X1: set_se1612935105at_nat] :
( ( $true != $true )
| ( $true = vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK21,X0),X1)),X1) )
| ( $true != vAPP(set_se1612935105at_nat,$o,finite1457549322at_nat,X1) )
| ( $false = vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X0),X1) ) )
| ~ spl155_2
| ~ spl155_29 ),
inference(superposition,[],[f2951,f2740]) ).
thf(f2951,plain,
( ! [X0: set_se1612935105at_nat,X1: set_Pr1986765409at_nat] :
( ( $true != vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X1),X0) )
| ( $true = vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK21,X1),X0)),X0) )
| ( $true != vAPP(set_se1612935105at_nat,$o,finite1457549322at_nat,X0) ) )
| ~ spl155_29 ),
inference(avatar_component_clause,[],[f2950]) ).
thf(f9225,plain,
( spl155_424
| ~ spl155_2
| ~ spl155_28 ),
inference(avatar_split_clause,[],[f2962,f2946,f2739,f9223]) ).
thf(f9223,plain,
( spl155_424
<=> ! [X0: set_Pr1986765409at_nat,X1: set_se1612935105at_nat] :
( ( $true = vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK20,X0),X1)),X1) )
| ( $true != vAPP(set_se1612935105at_nat,$o,finite1457549322at_nat,X1) )
| ( $false = vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_424])]) ).
thf(f2946,plain,
( spl155_28
<=> ! [X0: set_se1612935105at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK20,X1),X0)),X0) )
| ( $true != vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X1),X0) )
| ( $true != vAPP(set_se1612935105at_nat,$o,finite1457549322at_nat,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_28])]) ).
thf(f2962,plain,
( ! [X0: set_Pr1986765409at_nat,X1: set_se1612935105at_nat] :
( ( $true = vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK20,X0),X1)),X1) )
| ( $true != vAPP(set_se1612935105at_nat,$o,finite1457549322at_nat,X1) )
| ( $false = vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X0),X1) ) )
| ~ spl155_2
| ~ spl155_28 ),
inference(trivial_inequality_removal,[],[f2961]) ).
thf(f2961,plain,
( ! [X0: set_Pr1986765409at_nat,X1: set_se1612935105at_nat] :
( ( $true != $true )
| ( $true = vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK20,X0),X1)),X1) )
| ( $true != vAPP(set_se1612935105at_nat,$o,finite1457549322at_nat,X1) )
| ( $false = vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X0),X1) ) )
| ~ spl155_2
| ~ spl155_28 ),
inference(superposition,[],[f2947,f2740]) ).
thf(f2947,plain,
( ! [X0: set_se1612935105at_nat,X1: set_Pr1986765409at_nat] :
( ( $true != vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X1),X0) )
| ( $true = vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK20,X1),X0)),X0) )
| ( $true != vAPP(set_se1612935105at_nat,$o,finite1457549322at_nat,X0) ) )
| ~ spl155_28 ),
inference(avatar_component_clause,[],[f2946]) ).
thf(f9221,plain,
( spl155_423
| ~ spl155_2
| ~ spl155_27 ),
inference(avatar_split_clause,[],[f2956,f2942,f2739,f9219]) ).
thf(f9219,plain,
( spl155_423
<=> ! [X0: set_nat,X1: set_set_nat] :
( ( $true = vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,vAPP(set_set_nat,set_nat,vAPP(set_nat,sTfun(set_set_nat,set_nat),sK19,X0),X1)),X1) )
| ( $true != vAPP(set_set_nat,$o,finite2012248349et_nat,X1) )
| ( $false = vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_423])]) ).
thf(f2942,plain,
( spl155_27
<=> ! [X0: set_set_nat,X1: set_nat] :
( ( $true = vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,vAPP(set_set_nat,set_nat,vAPP(set_nat,sTfun(set_set_nat,set_nat),sK19,X1),X0)),X0) )
| ( $true != vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X1),X0) )
| ( $true != vAPP(set_set_nat,$o,finite2012248349et_nat,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_27])]) ).
thf(f2956,plain,
( ! [X0: set_nat,X1: set_set_nat] :
( ( $true = vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,vAPP(set_set_nat,set_nat,vAPP(set_nat,sTfun(set_set_nat,set_nat),sK19,X0),X1)),X1) )
| ( $true != vAPP(set_set_nat,$o,finite2012248349et_nat,X1) )
| ( $false = vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X0),X1) ) )
| ~ spl155_2
| ~ spl155_27 ),
inference(trivial_inequality_removal,[],[f2955]) ).
thf(f2955,plain,
( ! [X0: set_nat,X1: set_set_nat] :
( ( $true != $true )
| ( $true = vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,vAPP(set_set_nat,set_nat,vAPP(set_nat,sTfun(set_set_nat,set_nat),sK19,X0),X1)),X1) )
| ( $true != vAPP(set_set_nat,$o,finite2012248349et_nat,X1) )
| ( $false = vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X0),X1) ) )
| ~ spl155_2
| ~ spl155_27 ),
inference(superposition,[],[f2943,f2740]) ).
thf(f2943,plain,
( ! [X0: set_set_nat,X1: set_nat] :
( ( $true != vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X1),X0) )
| ( $true = vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,vAPP(set_set_nat,set_nat,vAPP(set_nat,sTfun(set_set_nat,set_nat),sK19,X1),X0)),X0) )
| ( $true != vAPP(set_set_nat,$o,finite2012248349et_nat,X0) ) )
| ~ spl155_27 ),
inference(avatar_component_clause,[],[f2942]) ).
thf(f9217,plain,
( spl155_422
| ~ spl155_2
| ~ spl155_26 ),
inference(avatar_split_clause,[],[f2954,f2938,f2739,f9215]) ).
thf(f9215,plain,
( spl155_422
<=> ! [X0: set_nat,X1: set_set_nat] :
( ( $true = vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,vAPP(set_set_nat,set_nat,vAPP(set_nat,sTfun(set_set_nat,set_nat),sK18,X0),X1)),X1) )
| ( $true != vAPP(set_set_nat,$o,finite2012248349et_nat,X1) )
| ( $false = vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_422])]) ).
thf(f2938,plain,
( spl155_26
<=> ! [X0: set_set_nat,X1: set_nat] :
( ( $true = vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,vAPP(set_set_nat,set_nat,vAPP(set_nat,sTfun(set_set_nat,set_nat),sK18,X1),X0)),X0) )
| ( $true != vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X1),X0) )
| ( $true != vAPP(set_set_nat,$o,finite2012248349et_nat,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_26])]) ).
thf(f2954,plain,
( ! [X0: set_nat,X1: set_set_nat] :
( ( $true = vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,vAPP(set_set_nat,set_nat,vAPP(set_nat,sTfun(set_set_nat,set_nat),sK18,X0),X1)),X1) )
| ( $true != vAPP(set_set_nat,$o,finite2012248349et_nat,X1) )
| ( $false = vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X0),X1) ) )
| ~ spl155_2
| ~ spl155_26 ),
inference(trivial_inequality_removal,[],[f2953]) ).
thf(f2953,plain,
( ! [X0: set_nat,X1: set_set_nat] :
( ( $true != $true )
| ( $true = vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,vAPP(set_set_nat,set_nat,vAPP(set_nat,sTfun(set_set_nat,set_nat),sK18,X0),X1)),X1) )
| ( $true != vAPP(set_set_nat,$o,finite2012248349et_nat,X1) )
| ( $false = vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X0),X1) ) )
| ~ spl155_2
| ~ spl155_26 ),
inference(superposition,[],[f2939,f2740]) ).
thf(f2939,plain,
( ! [X0: set_set_nat,X1: set_nat] :
( ( $true != vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X1),X0) )
| ( $true = vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,vAPP(set_set_nat,set_nat,vAPP(set_nat,sTfun(set_set_nat,set_nat),sK18,X1),X0)),X0) )
| ( $true != vAPP(set_set_nat,$o,finite2012248349et_nat,X0) ) )
| ~ spl155_26 ),
inference(avatar_component_clause,[],[f2938]) ).
thf(f9193,plain,
( spl155_421
| ~ spl155_181
| ~ spl155_378 ),
inference(avatar_split_clause,[],[f8177,f7987,f4909,f9191]) ).
thf(f9191,plain,
( spl155_421
<=> ! [X0: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p))),edges)) )
| ( $false = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_421])]) ).
thf(f7987,plain,
( spl155_378
<=> ! [X0: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p))) )
| ( $false = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_378])]) ).
thf(f8177,plain,
( ! [X0: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p))),edges)) )
| ( $false = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),X0) ) )
| ~ spl155_181
| ~ spl155_378 ),
inference(trivial_inequality_removal,[],[f8174]) ).
thf(f8174,plain,
( ! [X0: set_Pr1986765409at_nat] :
( ( $true != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p))),edges)) )
| ( $false = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),X0) ) )
| ~ spl155_181
| ~ spl155_378 ),
inference(superposition,[],[f4910,f7988]) ).
thf(f7988,plain,
( ! [X0: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p))) )
| ( $false = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),X0) ) )
| ~ spl155_378 ),
inference(avatar_component_clause,[],[f7987]) ).
thf(f9032,plain,
( spl155_420
| ~ spl155_249
| ~ spl155_257 ),
inference(avatar_split_clause,[],[f6250,f6217,f6162,f9030]) ).
thf(f9030,plain,
( spl155_420
<=> ! [X2: nat,X0: product_prod_nat_nat > a,X1: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),outgoing_a,X0),X1)) )
| ( vAPP(set_nat,nat,finite_card_nat,vAPP(set_nat,set_nat,vAPP(nat,sTfun(set_nat,set_nat),sK10,X2),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0))) = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_420])]) ).
thf(f6217,plain,
( spl155_257
<=> ! [X0: product_prod_nat_nat > a,X1: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),outgoing_a,X0),X1)) )
| ( $true != vAPP(set_nat,$o,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB))))),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_257])]) ).
thf(f6250,plain,
( ! [X2: nat,X0: product_prod_nat_nat > a,X1: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),outgoing_a,X0),X1)) )
| ( vAPP(set_nat,nat,finite_card_nat,vAPP(set_nat,set_nat,vAPP(nat,sTfun(set_nat,set_nat),sK10,X2),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0))) = X2 ) )
| ~ spl155_249
| ~ spl155_257 ),
inference(trivial_inequality_removal,[],[f6245]) ).
thf(f6245,plain,
( ! [X2: nat,X0: product_prod_nat_nat > a,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),outgoing_a,X0),X1)) )
| ( vAPP(set_nat,nat,finite_card_nat,vAPP(set_nat,set_nat,vAPP(nat,sTfun(set_nat,set_nat),sK10,X2),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0))) = X2 ) )
| ~ spl155_249
| ~ spl155_257 ),
inference(superposition,[],[f6218,f6163]) ).
thf(f6218,plain,
( ! [X0: product_prod_nat_nat > a,X1: nat] :
( ( $true != vAPP(set_nat,$o,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB))))),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),outgoing_a,X0),X1)) ) )
| ~ spl155_257 ),
inference(avatar_component_clause,[],[f6217]) ).
thf(f9010,plain,
( spl155_419
| ~ spl155_249
| ~ spl155_256 ),
inference(avatar_split_clause,[],[f6242,f6213,f6162,f9008]) ).
thf(f9008,plain,
( spl155_419
<=> ! [X2: nat,X0: product_prod_nat_nat > a,X1: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),incoming_a,X0),X1)) )
| ( vAPP(set_nat,nat,finite_card_nat,vAPP(set_nat,set_nat,vAPP(nat,sTfun(set_nat,set_nat),sK10,X2),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0))) = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_419])]) ).
thf(f6213,plain,
( spl155_256
<=> ! [X0: product_prod_nat_nat > a,X1: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),incoming_a,X0),X1)) )
| ( $true != vAPP(set_nat,$o,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB))))),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_256])]) ).
thf(f6242,plain,
( ! [X2: nat,X0: product_prod_nat_nat > a,X1: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),incoming_a,X0),X1)) )
| ( vAPP(set_nat,nat,finite_card_nat,vAPP(set_nat,set_nat,vAPP(nat,sTfun(set_nat,set_nat),sK10,X2),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0))) = X2 ) )
| ~ spl155_249
| ~ spl155_256 ),
inference(trivial_inequality_removal,[],[f6237]) ).
thf(f6237,plain,
( ! [X2: nat,X0: product_prod_nat_nat > a,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),incoming_a,X0),X1)) )
| ( vAPP(set_nat,nat,finite_card_nat,vAPP(set_nat,set_nat,vAPP(nat,sTfun(set_nat,set_nat),sK10,X2),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0))) = X2 ) )
| ~ spl155_249
| ~ spl155_256 ),
inference(superposition,[],[f6214,f6163]) ).
thf(f6214,plain,
( ! [X0: product_prod_nat_nat > a,X1: nat] :
( ( $true != vAPP(set_nat,$o,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB))))),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),incoming_a,X0),X1)) ) )
| ~ spl155_256 ),
inference(avatar_component_clause,[],[f6213]) ).
thf(f9006,plain,
( spl155_418
| ~ spl155_249
| ~ spl155_255 ),
inference(avatar_split_clause,[],[f6234,f6209,f6162,f9004]) ).
thf(f9004,plain,
( spl155_418
<=> ! [X2: nat,X0: product_prod_nat_nat > a,X1: set_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),incoming_a2,X0),X1)) )
| ( vAPP(set_nat,nat,finite_card_nat,vAPP(set_nat,set_nat,vAPP(nat,sTfun(set_nat,set_nat),sK10,X2),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0))) = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_418])]) ).
thf(f6209,plain,
( spl155_255
<=> ! [X0: product_prod_nat_nat > a,X1: set_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),incoming_a2,X0),X1)) )
| ( $true != vAPP(set_nat,$o,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB))))),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_255])]) ).
thf(f6234,plain,
( ! [X2: nat,X0: product_prod_nat_nat > a,X1: set_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),incoming_a2,X0),X1)) )
| ( vAPP(set_nat,nat,finite_card_nat,vAPP(set_nat,set_nat,vAPP(nat,sTfun(set_nat,set_nat),sK10,X2),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0))) = X2 ) )
| ~ spl155_249
| ~ spl155_255 ),
inference(trivial_inequality_removal,[],[f6229]) ).
thf(f6229,plain,
( ! [X2: nat,X0: product_prod_nat_nat > a,X1: set_nat] :
( ( $true != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),incoming_a2,X0),X1)) )
| ( vAPP(set_nat,nat,finite_card_nat,vAPP(set_nat,set_nat,vAPP(nat,sTfun(set_nat,set_nat),sK10,X2),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0))) = X2 ) )
| ~ spl155_249
| ~ spl155_255 ),
inference(superposition,[],[f6210,f6163]) ).
thf(f6210,plain,
( ! [X0: product_prod_nat_nat > a,X1: set_nat] :
( ( $true != vAPP(set_nat,$o,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB))))),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),incoming_a2,X0),X1)) ) )
| ~ spl155_255 ),
inference(avatar_component_clause,[],[f6209]) ).
thf(f9002,plain,
( spl155_417
| ~ spl155_249
| ~ spl155_254 ),
inference(avatar_split_clause,[],[f6226,f6205,f6162,f9000]) ).
thf(f9000,plain,
( spl155_417
<=> ! [X2: nat,X0: product_prod_nat_nat > a,X1: set_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),outgoing_a2,X0),X1)) )
| ( vAPP(set_nat,nat,finite_card_nat,vAPP(set_nat,set_nat,vAPP(nat,sTfun(set_nat,set_nat),sK10,X2),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0))) = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_417])]) ).
thf(f6205,plain,
( spl155_254
<=> ! [X0: product_prod_nat_nat > a,X1: set_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),outgoing_a2,X0),X1)) )
| ( $true != vAPP(set_nat,$o,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB))))),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_254])]) ).
thf(f6226,plain,
( ! [X2: nat,X0: product_prod_nat_nat > a,X1: set_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),outgoing_a2,X0),X1)) )
| ( vAPP(set_nat,nat,finite_card_nat,vAPP(set_nat,set_nat,vAPP(nat,sTfun(set_nat,set_nat),sK10,X2),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0))) = X2 ) )
| ~ spl155_249
| ~ spl155_254 ),
inference(trivial_inequality_removal,[],[f6221]) ).
thf(f6221,plain,
( ! [X2: nat,X0: product_prod_nat_nat > a,X1: set_nat] :
( ( $true != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),outgoing_a2,X0),X1)) )
| ( vAPP(set_nat,nat,finite_card_nat,vAPP(set_nat,set_nat,vAPP(nat,sTfun(set_nat,set_nat),sK10,X2),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0))) = X2 ) )
| ~ spl155_249
| ~ spl155_254 ),
inference(superposition,[],[f6206,f6163]) ).
thf(f6206,plain,
( ! [X0: product_prod_nat_nat > a,X1: set_nat] :
( ( $true != vAPP(set_nat,$o,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB))))),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),outgoing_a2,X0),X1)) ) )
| ~ spl155_254 ),
inference(avatar_component_clause,[],[f6205]) ).
thf(f8998,plain,
( spl155_416
| ~ spl155_92
| ~ spl155_105 ),
inference(avatar_split_clause,[],[f3591,f3488,f3386,f8996]) ).
thf(f8996,plain,
( spl155_416
<=> ! [X0: set_nat,X1: set_Pr1986765409at_nat] :
( ( vAPP(set_nat,nat,finite_card_nat,X0) = vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK28,X1),vAPP(set_nat,nat,finite_card_nat,X0))) )
| ( $true = vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,X0),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_416])]) ).
thf(f3591,plain,
( ! [X0: set_nat,X1: set_Pr1986765409at_nat] :
( ( vAPP(set_nat,nat,finite_card_nat,X0) = vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK28,X1),vAPP(set_nat,nat,finite_card_nat,X0))) )
| ( $true = vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,X0),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)) ) )
| ~ spl155_92
| ~ spl155_105 ),
inference(trivial_inequality_removal,[],[f3586]) ).
thf(f3586,plain,
( ! [X0: set_nat,X1: set_Pr1986765409at_nat] :
( ( $true != $true )
| ( vAPP(set_nat,nat,finite_card_nat,X0) = vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK28,X1),vAPP(set_nat,nat,finite_card_nat,X0))) )
| ( $true = vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,X0),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)) ) )
| ~ spl155_92
| ~ spl155_105 ),
inference(superposition,[],[f3489,f3387]) ).
thf(f8994,plain,
( spl155_415
| ~ spl155_94
| ~ spl155_105 ),
inference(avatar_split_clause,[],[f3590,f3488,f3394,f8992]) ).
thf(f8992,plain,
( spl155_415
<=> ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0) = vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK28,X1),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0))) )
| ( $true = vAPP(nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(nat,$o),sP1,X0),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_415])]) ).
thf(f3590,plain,
( ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0) = vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK28,X1),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0))) )
| ( $true = vAPP(nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(nat,$o),sP1,X0),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)) ) )
| ~ spl155_94
| ~ spl155_105 ),
inference(trivial_inequality_removal,[],[f3587]) ).
thf(f3587,plain,
( ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true != $true )
| ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0) = vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK28,X1),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0))) )
| ( $true = vAPP(nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(nat,$o),sP1,X0),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)) ) )
| ~ spl155_94
| ~ spl155_105 ),
inference(superposition,[],[f3489,f3395]) ).
thf(f8990,plain,
( spl155_414
| ~ spl155_92
| ~ spl155_103 ),
inference(avatar_split_clause,[],[f3559,f3480,f3386,f8988]) ).
thf(f8988,plain,
( spl155_414
<=> ! [X0: set_nat,X1: set_nat] :
( ( vAPP(set_nat,nat,finite_card_nat,X0) = vAPP(set_nat,nat,finite_card_nat,vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK27,X1),vAPP(set_nat,nat,finite_card_nat,X0))) )
| ( $true = vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,X0),vAPP(set_nat,nat,finite_card_nat,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_414])]) ).
thf(f3559,plain,
( ! [X0: set_nat,X1: set_nat] :
( ( vAPP(set_nat,nat,finite_card_nat,X0) = vAPP(set_nat,nat,finite_card_nat,vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK27,X1),vAPP(set_nat,nat,finite_card_nat,X0))) )
| ( $true = vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,X0),vAPP(set_nat,nat,finite_card_nat,X1)) ) )
| ~ spl155_92
| ~ spl155_103 ),
inference(trivial_inequality_removal,[],[f3554]) ).
thf(f3554,plain,
( ! [X0: set_nat,X1: set_nat] :
( ( $true != $true )
| ( vAPP(set_nat,nat,finite_card_nat,X0) = vAPP(set_nat,nat,finite_card_nat,vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK27,X1),vAPP(set_nat,nat,finite_card_nat,X0))) )
| ( $true = vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,X0),vAPP(set_nat,nat,finite_card_nat,X1)) ) )
| ~ spl155_92
| ~ spl155_103 ),
inference(superposition,[],[f3481,f3387]) ).
thf(f8986,plain,
( spl155_413
| ~ spl155_94
| ~ spl155_103 ),
inference(avatar_split_clause,[],[f3558,f3480,f3394,f8984]) ).
thf(f8984,plain,
( spl155_413
<=> ! [X0: set_Pr1986765409at_nat,X1: set_nat] :
( ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0) = vAPP(set_nat,nat,finite_card_nat,vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK27,X1),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0))) )
| ( $true = vAPP(nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(nat,$o),sP1,X0),vAPP(set_nat,nat,finite_card_nat,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_413])]) ).
thf(f3558,plain,
( ! [X0: set_Pr1986765409at_nat,X1: set_nat] :
( ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0) = vAPP(set_nat,nat,finite_card_nat,vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK27,X1),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0))) )
| ( $true = vAPP(nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(nat,$o),sP1,X0),vAPP(set_nat,nat,finite_card_nat,X1)) ) )
| ~ spl155_94
| ~ spl155_103 ),
inference(trivial_inequality_removal,[],[f3555]) ).
thf(f3555,plain,
( ! [X0: set_Pr1986765409at_nat,X1: set_nat] :
( ( $true != $true )
| ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0) = vAPP(set_nat,nat,finite_card_nat,vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK27,X1),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0))) )
| ( $true = vAPP(nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(nat,$o),sP1,X0),vAPP(set_nat,nat,finite_card_nat,X1)) ) )
| ~ spl155_94
| ~ spl155_103 ),
inference(superposition,[],[f3481,f3395]) ).
thf(f8982,plain,
( spl155_412
| ~ spl155_8
| ~ spl155_32 ),
inference(avatar_split_clause,[],[f2983,f2973,f2801,f8980]) ).
thf(f8980,plain,
( spl155_412
<=> ! [X0: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,s),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,c))) )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,s),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_412])]) ).
thf(f2983,plain,
( ! [X0: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,s),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,c))) )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,s),X0) ) )
| ~ spl155_8
| ~ spl155_32 ),
inference(trivial_inequality_removal,[],[f2980]) ).
thf(f2980,plain,
( ! [X0: set_nat] :
( ( $true != $true )
| ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,s),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,c))) )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,s),X0) ) )
| ~ spl155_8
| ~ spl155_32 ),
inference(superposition,[],[f2974,f2803]) ).
thf(f8978,plain,
( spl155_411
| ~ spl155_2
| ~ spl155_25 ),
inference(avatar_split_clause,[],[f2936,f2932,f2739,f8976]) ).
thf(f8976,plain,
( spl155_411
<=> ! [X2: nat,X0: list_P559422087at_nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,nat)),sK64,X0),X1),X2) = X1 )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,$o)),sP7,X0),X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_411])]) ).
thf(f2932,plain,
( spl155_25
<=> ! [X2: list_P559422087at_nat,X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,nat)),sK64,X2),X1),X0) = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,$o)),sP7,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_25])]) ).
thf(f2936,plain,
( ! [X2: nat,X0: list_P559422087at_nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,nat)),sK64,X0),X1),X2) = X1 )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,$o)),sP7,X0),X1),X2) ) )
| ~ spl155_2
| ~ spl155_25 ),
inference(trivial_inequality_removal,[],[f2935]) ).
thf(f2935,plain,
( ! [X2: nat,X0: list_P559422087at_nat,X1: nat] :
( ( $true != $true )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,nat)),sK64,X0),X1),X2) = X1 )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,$o)),sP7,X0),X1),X2) ) )
| ~ spl155_2
| ~ spl155_25 ),
inference(superposition,[],[f2933,f2740]) ).
thf(f2933,plain,
( ! [X2: list_P559422087at_nat,X0: nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,$o)),sP7,X2),X1),X0) )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,nat)),sK64,X2),X1),X0) = X1 ) )
| ~ spl155_25 ),
inference(avatar_component_clause,[],[f2932]) ).
thf(f8630,plain,
( spl155_410
| ~ spl155_76
| ~ spl155_102 ),
inference(avatar_split_clause,[],[f3546,f3476,f3244,f8628]) ).
thf(f8628,plain,
( spl155_410
<=> ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0) != vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1)) )
| ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1) = X0 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_410])]) ).
thf(f3546,plain,
( ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0) != vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1)) )
| ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1) = X0 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) ) )
| ~ spl155_76
| ~ spl155_102 ),
inference(trivial_inequality_removal,[],[f3528]) ).
thf(f3528,plain,
( ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true != $true )
| ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0) != vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1)) )
| ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1) = X0 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) ) )
| ~ spl155_76
| ~ spl155_102 ),
inference(superposition,[],[f3477,f3245]) ).
thf(f8626,plain,
( spl155_409
| ~ spl155_77
| ~ spl155_102 ),
inference(avatar_split_clause,[],[f3545,f3476,f3248,f8624]) ).
thf(f8624,plain,
( spl155_409
<=> ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1) != vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1)) )
| ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1) = X1 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_409])]) ).
thf(f3545,plain,
( ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1) != vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1)) )
| ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1) = X1 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X1) ) )
| ~ spl155_77
| ~ spl155_102 ),
inference(trivial_inequality_removal,[],[f3529]) ).
thf(f3529,plain,
( ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true != $true )
| ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1) != vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1)) )
| ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1) = X1 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X1) ) )
| ~ spl155_77
| ~ spl155_102 ),
inference(superposition,[],[f3477,f3249]) ).
thf(f8622,plain,
( spl155_408
| ~ spl155_2
| ~ spl155_24 ),
inference(avatar_split_clause,[],[f2924,f2914,f2739,f8620]) ).
thf(f8620,plain,
( spl155_408
<=> ! [X2: nat,X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK61,X2),X0)) )
| ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK60,X0)) )
| ( $false = vAPP(nat,$o,X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_408])]) ).
thf(f2924,plain,
( ! [X2: nat,X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK61,X2),X0)) )
| ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK60,X0)) )
| ( $false = vAPP(nat,$o,X0,X1) ) )
| ~ spl155_2
| ~ spl155_24 ),
inference(trivial_inequality_removal,[],[f2923]) ).
thf(f2923,plain,
( ! [X2: nat,X0: nat > $o,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK61,X2),X0)) )
| ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK60,X0)) )
| ( $false = vAPP(nat,$o,X0,X1) ) )
| ~ spl155_2
| ~ spl155_24 ),
inference(superposition,[],[f2915,f2740]) ).
thf(f8562,plain,
( spl155_407
| ~ spl155_89
| ~ spl155_91 ),
inference(avatar_split_clause,[],[f3401,f3382,f3301,f8560]) ).
thf(f8560,plain,
( spl155_407
<=> ! [X0: nat,X1: set_Pr1986765409at_nat] :
( ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sK11,X0),X1) = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sK11,X0),X1)),X1) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_407])]) ).
thf(f3401,plain,
( ! [X0: nat,X1: set_Pr1986765409at_nat] :
( ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sK11,X0),X1) = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sK11,X0),X1)),X1) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X1) ) )
| ~ spl155_89
| ~ spl155_91 ),
inference(trivial_inequality_removal,[],[f3398]) ).
thf(f3398,plain,
( ! [X0: nat,X1: set_Pr1986765409at_nat] :
( ( $true != $true )
| ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sK11,X0),X1) = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sK11,X0),X1)),X1) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X1) ) )
| ~ spl155_89
| ~ spl155_91 ),
inference(superposition,[],[f3302,f3383]) ).
thf(f8558,plain,
( spl155_406
| ~ spl155_88
| ~ spl155_91 ),
inference(avatar_split_clause,[],[f3400,f3382,f3297,f8556]) ).
thf(f8556,plain,
( spl155_406
<=> ! [X0: nat,X1: set_Pr1986765409at_nat] :
( ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sK11,X0),X1) = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sK11,X0),X1)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_406])]) ).
thf(f3400,plain,
( ! [X0: nat,X1: set_Pr1986765409at_nat] :
( ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sK11,X0),X1) = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sK11,X0),X1)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X1) ) )
| ~ spl155_88
| ~ spl155_91 ),
inference(trivial_inequality_removal,[],[f3399]) ).
thf(f3399,plain,
( ! [X0: nat,X1: set_Pr1986765409at_nat] :
( ( $true != $true )
| ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sK11,X0),X1) = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sK11,X0),X1)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X1) ) )
| ~ spl155_88
| ~ spl155_91 ),
inference(superposition,[],[f3298,f3383]) ).
thf(f8554,plain,
( spl155_405
| ~ spl155_191
| ~ spl155_370 ),
inference(avatar_split_clause,[],[f7832,f7694,f5209,f8552]) ).
thf(f8552,plain,
( spl155_405
<=> ! [X0: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),edges)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p))) )
| ( $false = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_405])]) ).
thf(f5209,plain,
( spl155_191
<=> ! [X0: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),edges)) )
| ( $false = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_191])]) ).
thf(f7832,plain,
( ! [X0: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),edges)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p))) )
| ( $false = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),X0) ) )
| ~ spl155_191
| ~ spl155_370 ),
inference(trivial_inequality_removal,[],[f7822]) ).
thf(f7822,plain,
( ! [X0: set_Pr1986765409at_nat] :
( ( $true != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),edges)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p))) )
| ( $false = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),X0) ) )
| ~ spl155_191
| ~ spl155_370 ),
inference(superposition,[],[f7695,f5210]) ).
thf(f5210,plain,
( ! [X0: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),edges)) )
| ( $false = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),X0) ) )
| ~ spl155_191 ),
inference(avatar_component_clause,[],[f5209]) ).
thf(f8550,plain,
( spl155_404
| ~ spl155_24 ),
inference(avatar_split_clause,[],[f2930,f2914,f8548]) ).
thf(f8548,plain,
( spl155_404
<=> ! [X0: nat,X1: nat] :
( ( vAPP(sTfun(nat,$o),nat,sK60,vAPP(nat,sTfun(nat,$o),vEQ(nat),X1)) = X1 )
| ( vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK61,X0),vAPP(nat,sTfun(nat,$o),vEQ(nat),X1)) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_404])]) ).
thf(f2930,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(sTfun(nat,$o),nat,sK60,vAPP(nat,sTfun(nat,$o),vEQ(nat),X1)) = X1 )
| ( vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK61,X0),vAPP(nat,sTfun(nat,$o),vEQ(nat),X1)) = X1 ) )
| ~ spl155_24 ),
inference(equality_proxy_clausification,[],[f2917]) ).
thf(f2917,plain,
( ! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X1),vAPP(sTfun(nat,$o),nat,sK60,vAPP(nat,sTfun(nat,$o),vEQ(nat),X1))) )
| ( vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK61,X0),vAPP(nat,sTfun(nat,$o),vEQ(nat),X1)) = X1 ) )
| ~ spl155_24 ),
inference(leibniz_equality_elimination,[],[f2915]) ).
thf(f8430,plain,
( spl155_403
| ~ spl155_248
| ~ spl155_257 ),
inference(avatar_split_clause,[],[f6249,f6217,f6148,f8428]) ).
thf(f8428,plain,
( spl155_403
<=> ! [X2: nat,X0: product_prod_nat_nat > a,X1: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),outgoing_a,X0),X1)) )
| ( $true = vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0)),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_403])]) ).
thf(f6249,plain,
( ! [X2: nat,X0: product_prod_nat_nat > a,X1: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),outgoing_a,X0),X1)) )
| ( $true = vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0)),X2) ) )
| ~ spl155_248
| ~ spl155_257 ),
inference(trivial_inequality_removal,[],[f6246]) ).
thf(f6246,plain,
( ! [X2: nat,X0: product_prod_nat_nat > a,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),outgoing_a,X0),X1)) )
| ( $true = vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0)),X2) ) )
| ~ spl155_248
| ~ spl155_257 ),
inference(superposition,[],[f6218,f6149]) ).
thf(f8426,plain,
( spl155_402
| ~ spl155_344
| ~ spl155_370 ),
inference(avatar_split_clause,[],[f7831,f7694,f7452,f8424]) ).
thf(f8424,plain,
( spl155_402
<=> ! [X0: product_prod_nat_nat > $o] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X0)),edges)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p))) )
| ( $false = vAPP(product_prod_nat_nat,$o,X0,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_402])]) ).
thf(f7831,plain,
( ! [X0: product_prod_nat_nat > $o] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X0)),edges)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p))) )
| ( $false = vAPP(product_prod_nat_nat,$o,X0,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)) ) )
| ~ spl155_344
| ~ spl155_370 ),
inference(trivial_inequality_removal,[],[f7823]) ).
thf(f7823,plain,
( ! [X0: product_prod_nat_nat > $o] :
( ( $true != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X0)),edges)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p))) )
| ( $false = vAPP(product_prod_nat_nat,$o,X0,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)) ) )
| ~ spl155_344
| ~ spl155_370 ),
inference(superposition,[],[f7695,f7453]) ).
thf(f8422,plain,
( spl155_401
| ~ spl155_248
| ~ spl155_256 ),
inference(avatar_split_clause,[],[f6241,f6213,f6148,f8420]) ).
thf(f8420,plain,
( spl155_401
<=> ! [X2: nat,X0: product_prod_nat_nat > a,X1: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),incoming_a,X0),X1)) )
| ( $true = vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0)),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_401])]) ).
thf(f6241,plain,
( ! [X2: nat,X0: product_prod_nat_nat > a,X1: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),incoming_a,X0),X1)) )
| ( $true = vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0)),X2) ) )
| ~ spl155_248
| ~ spl155_256 ),
inference(trivial_inequality_removal,[],[f6238]) ).
thf(f6238,plain,
( ! [X2: nat,X0: product_prod_nat_nat > a,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),incoming_a,X0),X1)) )
| ( $true = vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0)),X2) ) )
| ~ spl155_248
| ~ spl155_256 ),
inference(superposition,[],[f6214,f6149]) ).
thf(f8418,plain,
( spl155_400
| ~ spl155_248
| ~ spl155_255 ),
inference(avatar_split_clause,[],[f6233,f6209,f6148,f8416]) ).
thf(f8416,plain,
( spl155_400
<=> ! [X2: nat,X0: product_prod_nat_nat > a,X1: set_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),incoming_a2,X0),X1)) )
| ( $true = vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0)),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_400])]) ).
thf(f6233,plain,
( ! [X2: nat,X0: product_prod_nat_nat > a,X1: set_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),incoming_a2,X0),X1)) )
| ( $true = vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0)),X2) ) )
| ~ spl155_248
| ~ spl155_255 ),
inference(trivial_inequality_removal,[],[f6230]) ).
thf(f6230,plain,
( ! [X2: nat,X0: product_prod_nat_nat > a,X1: set_nat] :
( ( $true != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),incoming_a2,X0),X1)) )
| ( $true = vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0)),X2) ) )
| ~ spl155_248
| ~ spl155_255 ),
inference(superposition,[],[f6210,f6149]) ).
thf(f8414,plain,
( spl155_399
| ~ spl155_248
| ~ spl155_254 ),
inference(avatar_split_clause,[],[f6225,f6205,f6148,f8412]) ).
thf(f8412,plain,
( spl155_399
<=> ! [X2: nat,X0: product_prod_nat_nat > a,X1: set_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),outgoing_a2,X0),X1)) )
| ( $true = vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0)),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_399])]) ).
thf(f6225,plain,
( ! [X2: nat,X0: product_prod_nat_nat > a,X1: set_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),outgoing_a2,X0),X1)) )
| ( $true = vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0)),X2) ) )
| ~ spl155_248
| ~ spl155_254 ),
inference(trivial_inequality_removal,[],[f6222]) ).
thf(f6222,plain,
( ! [X2: nat,X0: product_prod_nat_nat > a,X1: set_nat] :
( ( $true != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),outgoing_a2,X0),X1)) )
| ( $true = vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0)),X2) ) )
| ~ spl155_248
| ~ spl155_254 ),
inference(superposition,[],[f6206,f6149]) ).
thf(f8410,plain,
( spl155_398
| ~ spl155_79
| ~ spl155_122 ),
inference(avatar_split_clause,[],[f3742,f3702,f3260,f8408]) ).
thf(f8408,plain,
( spl155_398
<=> ! [X0: product_prod_nat_nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,c)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_398])]) ).
thf(f3742,plain,
( ! [X0: product_prod_nat_nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,c)) ) )
| ~ spl155_79
| ~ spl155_122 ),
inference(trivial_inequality_removal,[],[f3731]) ).
thf(f3731,plain,
( ! [X0: product_prod_nat_nat] :
( ( $true != $true )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,c)) ) )
| ~ spl155_79
| ~ spl155_122 ),
inference(superposition,[],[f3703,f3262]) ).
thf(f8406,plain,
( spl155_397
| ~ spl155_92
| ~ spl155_104 ),
inference(avatar_split_clause,[],[f3578,f3484,f3386,f8404]) ).
thf(f8404,plain,
( spl155_397
<=> ! [X0: set_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK28,X1),vAPP(set_nat,nat,finite_card_nat,X0))) )
| ( $true = vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,X0),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_397])]) ).
thf(f3578,plain,
( ! [X0: set_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK28,X1),vAPP(set_nat,nat,finite_card_nat,X0))) )
| ( $true = vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,X0),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)) ) )
| ~ spl155_92
| ~ spl155_104 ),
inference(trivial_inequality_removal,[],[f3573]) ).
thf(f3573,plain,
( ! [X0: set_nat,X1: set_Pr1986765409at_nat] :
( ( $true != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK28,X1),vAPP(set_nat,nat,finite_card_nat,X0))) )
| ( $true = vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,X0),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)) ) )
| ~ spl155_92
| ~ spl155_104 ),
inference(superposition,[],[f3485,f3387]) ).
thf(f8402,plain,
( spl155_396
| ~ spl155_94
| ~ spl155_104 ),
inference(avatar_split_clause,[],[f3577,f3484,f3394,f8400]) ).
thf(f8400,plain,
( spl155_396
<=> ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK28,X1),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0))) )
| ( $true = vAPP(nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(nat,$o),sP1,X0),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_396])]) ).
thf(f3577,plain,
( ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK28,X1),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0))) )
| ( $true = vAPP(nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(nat,$o),sP1,X0),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)) ) )
| ~ spl155_94
| ~ spl155_104 ),
inference(trivial_inequality_removal,[],[f3574]) ).
thf(f3574,plain,
( ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK28,X1),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0))) )
| ( $true = vAPP(nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(nat,$o),sP1,X0),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)) ) )
| ~ spl155_94
| ~ spl155_104 ),
inference(superposition,[],[f3485,f3395]) ).
thf(f8398,plain,
( spl155_394
| ~ spl155_395
| ~ spl155_4
| ~ spl155_79
| ~ spl155_102 ),
inference(avatar_split_clause,[],[f3550,f3476,f3260,f2775,f8395,f8391]) ).
thf(f8395,plain,
( spl155_395
<=> ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,c)) = vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_395])]) ).
thf(f3550,plain,
( ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,c)) != vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) )
| ( vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c) = vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,c) )
| ~ spl155_4
| ~ spl155_79
| ~ spl155_102 ),
inference(trivial_inequality_removal,[],[f3549]) ).
thf(f3549,plain,
( ( $true != $true )
| ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,c)) != vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) )
| ( vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c) = vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,c) )
| ~ spl155_4
| ~ spl155_79
| ~ spl155_102 ),
inference(forward_demodulation,[],[f3543,f2777]) ).
thf(f3543,plain,
( ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,c)) != vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) )
| ( vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c) = vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,c) )
| ( vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,c)) != $true )
| ~ spl155_79
| ~ spl155_102 ),
inference(trivial_inequality_removal,[],[f3532]) ).
thf(f3532,plain,
( ( $true != $true )
| ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,c)) != vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) )
| ( vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c) = vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,c) )
| ( vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,c)) != $true )
| ~ spl155_79
| ~ spl155_102 ),
inference(superposition,[],[f3477,f3262]) ).
thf(f8389,plain,
( spl155_393
| ~ spl155_6
| ~ spl155_12 ),
inference(avatar_split_clause,[],[f2845,f2818,f2785,f8387]) ).
thf(f8387,plain,
( spl155_393
<=> ! [X0: nat,X1: set_Pr1986765409at_nat] :
( ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sK11,X0),X1) = vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,vAPP(set_Pr1986765409at_nat,list_P559422087at_nat,sK9,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sK11,X0),X1))) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_393])]) ).
thf(f2785,plain,
( spl155_6
<=> ! [X0: set_Pr1986765409at_nat] :
( ( vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,vAPP(set_Pr1986765409at_nat,list_P559422087at_nat,sK9,X0)) = X0 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_6])]) ).
thf(f2818,plain,
( spl155_12
<=> ! [X0: set_Pr1986765409at_nat,X1: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sK11,X1),X0)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_12])]) ).
thf(f2845,plain,
( ! [X0: nat,X1: set_Pr1986765409at_nat] :
( ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sK11,X0),X1) = vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,vAPP(set_Pr1986765409at_nat,list_P559422087at_nat,sK9,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sK11,X0),X1))) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X1) ) )
| ~ spl155_6
| ~ spl155_12 ),
inference(trivial_inequality_removal,[],[f2844]) ).
thf(f2844,plain,
( ! [X0: nat,X1: set_Pr1986765409at_nat] :
( ( $true != $true )
| ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sK11,X0),X1) = vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,vAPP(set_Pr1986765409at_nat,list_P559422087at_nat,sK9,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sK11,X0),X1))) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X1) ) )
| ~ spl155_6
| ~ spl155_12 ),
inference(superposition,[],[f2786,f2819]) ).
thf(f2819,plain,
( ! [X0: set_Pr1986765409at_nat,X1: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sK11,X1),X0)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) ) )
| ~ spl155_12 ),
inference(avatar_component_clause,[],[f2818]) ).
thf(f2786,plain,
( ! [X0: set_Pr1986765409at_nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) )
| ( vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,vAPP(set_Pr1986765409at_nat,list_P559422087at_nat,sK9,X0)) = X0 ) )
| ~ spl155_6 ),
inference(avatar_component_clause,[],[f2785]) ).
thf(f8317,plain,
( spl155_392
| ~ spl155_90
| ~ spl155_119 ),
inference(avatar_split_clause,[],[f3690,f3632,f3367,f8315]) ).
thf(f8315,plain,
( spl155_392
<=> ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X1) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,X1),X0)),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_392])]) ).
thf(f3690,plain,
( ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X1) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,X1),X0)),X0) ) )
| ~ spl155_90
| ~ spl155_119 ),
inference(trivial_inequality_removal,[],[f3672]) ).
thf(f3672,plain,
( ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X1) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,X1),X0)),X0) ) )
| ~ spl155_90
| ~ spl155_119 ),
inference(superposition,[],[f3368,f3633]) ).
thf(f8165,plain,
( spl155_391
| ~ spl155_249
| ~ spl155_250 ),
inference(avatar_split_clause,[],[f6184,f6171,f6162,f8163]) ).
thf(f8163,plain,
( spl155_391
<=> ! [X0: product_prod_nat_nat > a,X1: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) )
| ( vAPP(set_nat,nat,finite_card_nat,vAPP(set_nat,set_nat,vAPP(nat,sTfun(set_nat,set_nat),sK10,X1),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0))) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_391])]) ).
thf(f6171,plain,
( spl155_250
<=> ! [X0: product_prod_nat_nat > a] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) )
| ( $true != vAPP(set_nat,$o,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB))))),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_250])]) ).
thf(f6184,plain,
( ! [X0: product_prod_nat_nat > a,X1: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) )
| ( vAPP(set_nat,nat,finite_card_nat,vAPP(set_nat,set_nat,vAPP(nat,sTfun(set_nat,set_nat),sK10,X1),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0))) = X1 ) )
| ~ spl155_249
| ~ spl155_250 ),
inference(trivial_inequality_removal,[],[f6179]) ).
thf(f6179,plain,
( ! [X0: product_prod_nat_nat > a,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) )
| ( vAPP(set_nat,nat,finite_card_nat,vAPP(set_nat,set_nat,vAPP(nat,sTfun(set_nat,set_nat),sK10,X1),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0))) = X1 ) )
| ~ spl155_249
| ~ spl155_250 ),
inference(superposition,[],[f6172,f6163]) ).
thf(f6172,plain,
( ! [X0: product_prod_nat_nat > a] :
( ( $true != vAPP(set_nat,$o,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB))))),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) ) )
| ~ spl155_250 ),
inference(avatar_component_clause,[],[f6171]) ).
thf(f8161,plain,
( spl155_390
| ~ spl155_94
| ~ spl155_127 ),
inference(avatar_split_clause,[],[f3782,f3772,f3394,f8159]) ).
thf(f8159,plain,
( spl155_390
<=> ! [X0: set_Pr1986765409at_nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(nat,$o),sP1,X0),X1) )
| ( $true = vAPP(nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(nat,$o),sP1,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK17,X0),X1)),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_390])]) ).
thf(f3782,plain,
( ! [X0: set_Pr1986765409at_nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(nat,$o),sP1,X0),X1) )
| ( $true = vAPP(nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(nat,$o),sP1,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK17,X0),X1)),X1) ) )
| ~ spl155_94
| ~ spl155_127 ),
inference(trivial_inequality_removal,[],[f3779]) ).
thf(f3779,plain,
( ! [X0: set_Pr1986765409at_nat,X1: nat] :
( ( $true != $true )
| ( $true != vAPP(nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(nat,$o),sP1,X0),X1) )
| ( $true = vAPP(nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(nat,$o),sP1,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK17,X0),X1)),X1) ) )
| ~ spl155_94
| ~ spl155_127 ),
inference(superposition,[],[f3773,f3395]) ).
thf(f8157,plain,
( spl155_389
| ~ spl155_92
| ~ spl155_126 ),
inference(avatar_split_clause,[],[f3778,f3768,f3386,f8155]) ).
thf(f8155,plain,
( spl155_389
<=> ! [X0: set_nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,X0),X1) )
| ( $true = vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK14,X0),X1)),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_389])]) ).
thf(f3778,plain,
( ! [X0: set_nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,X0),X1) )
| ( $true = vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK14,X0),X1)),X1) ) )
| ~ spl155_92
| ~ spl155_126 ),
inference(trivial_inequality_removal,[],[f3775]) ).
thf(f3775,plain,
( ! [X0: set_nat,X1: nat] :
( ( $true != $true )
| ( $true != vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,X0),X1) )
| ( $true = vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK14,X0),X1)),X1) ) )
| ~ spl155_92
| ~ spl155_126 ),
inference(superposition,[],[f3769,f3387]) ).
thf(f8153,plain,
( spl155_388
| ~ spl155_89
| ~ spl155_119 ),
inference(avatar_split_clause,[],[f3689,f3632,f3301,f8151]) ).
thf(f8151,plain,
( spl155_388
<=> ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1) = X0 )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,X1),X0)),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_388])]) ).
thf(f3689,plain,
( ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1) = X0 )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,X1),X0)),X0) ) )
| ~ spl155_89
| ~ spl155_119 ),
inference(trivial_inequality_removal,[],[f3673]) ).
thf(f3673,plain,
( ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true != $true )
| ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1) = X0 )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,X1),X0)),X0) ) )
| ~ spl155_89
| ~ spl155_119 ),
inference(superposition,[],[f3302,f3633]) ).
thf(f8149,plain,
( spl155_387
| ~ spl155_88
| ~ spl155_119 ),
inference(avatar_split_clause,[],[f3688,f3632,f3297,f8147]) ).
thf(f8147,plain,
( spl155_387
<=> ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),X0) = X0 )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,X1),X0)),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_387])]) ).
thf(f3688,plain,
( ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),X0) = X0 )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,X1),X0)),X0) ) )
| ~ spl155_88
| ~ spl155_119 ),
inference(trivial_inequality_removal,[],[f3674]) ).
thf(f3674,plain,
( ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true != $true )
| ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),X0) = X0 )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,X1),X0)),X0) ) )
| ~ spl155_88
| ~ spl155_119 ),
inference(superposition,[],[f3298,f3633]) ).
thf(f8145,plain,
( spl155_386
| ~ spl155_85
| ~ spl155_117 ),
inference(avatar_split_clause,[],[f3659,f3624,f3285,f8143]) ).
thf(f8143,plain,
( spl155_386
<=> ! [X0: set_nat,X1: set_nat] :
( ( vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X1) = X0 )
| ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,vAPP(set_nat,nat,vAPP(set_nat,sTfun(set_nat,nat),sK15,X1),X0)),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_386])]) ).
thf(f3659,plain,
( ! [X0: set_nat,X1: set_nat] :
( ( vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X1) = X0 )
| ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,vAPP(set_nat,nat,vAPP(set_nat,sTfun(set_nat,nat),sK15,X1),X0)),X0) ) )
| ~ spl155_85
| ~ spl155_117 ),
inference(trivial_inequality_removal,[],[f3643]) ).
thf(f3643,plain,
( ! [X0: set_nat,X1: set_nat] :
( ( $true != $true )
| ( vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X1) = X0 )
| ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,vAPP(set_nat,nat,vAPP(set_nat,sTfun(set_nat,nat),sK15,X1),X0)),X0) ) )
| ~ spl155_85
| ~ spl155_117 ),
inference(superposition,[],[f3286,f3625]) ).
thf(f8141,plain,
( spl155_385
| ~ spl155_84
| ~ spl155_117 ),
inference(avatar_split_clause,[],[f3658,f3624,f3281,f8139]) ).
thf(f8139,plain,
( spl155_385
<=> ! [X0: set_nat,X1: set_nat] :
( ( vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),X0) = X0 )
| ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,vAPP(set_nat,nat,vAPP(set_nat,sTfun(set_nat,nat),sK15,X1),X0)),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_385])]) ).
thf(f3658,plain,
( ! [X0: set_nat,X1: set_nat] :
( ( vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),X0) = X0 )
| ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,vAPP(set_nat,nat,vAPP(set_nat,sTfun(set_nat,nat),sK15,X1),X0)),X0) ) )
| ~ spl155_84
| ~ spl155_117 ),
inference(trivial_inequality_removal,[],[f3644]) ).
thf(f3644,plain,
( ! [X0: set_nat,X1: set_nat] :
( ( $true != $true )
| ( vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),X0) = X0 )
| ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,vAPP(set_nat,nat,vAPP(set_nat,sTfun(set_nat,nat),sK15,X1),X0)),X0) ) )
| ~ spl155_84
| ~ spl155_117 ),
inference(superposition,[],[f3282,f3625]) ).
thf(f8137,plain,
spl155_384,
inference(avatar_split_clause,[],[f2708,f8135]) ).
thf(f8135,plain,
( spl155_384
<=> ! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( $false = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),nil_Pr1308055047at_nat),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_384])]) ).
thf(f2708,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( $false = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),nil_Pr1308055047at_nat),X1) ) ),
inference(equality_proxy_clausification,[],[f2705]) ).
thf(f2705,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) )
| ( $false = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),nil_Pr1308055047at_nat),X1) ) ),
inference(binary_proxy_clausification,[],[f1706]) ).
thf(f1706,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),nil_Pr1308055047at_nat),X1) ),
inference(cnf_transformation,[],[f503]) ).
thf(f503,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),nil_Pr1308055047at_nat),X1) ),
inference(fool_elimination,[],[f502]) ).
thf(f502,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),nil_Pr1308055047at_nat),X1)
= ( X0 = X1 ) ),
inference(rectify,[],[f350]) ).
thf(f350,axiom,
! [X1: nat,X7: nat] :
( vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X1),nil_Pr1308055047at_nat),X7)
= ( X1 = X7 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_349_isPath_Osimps_I1_J) ).
thf(f8133,plain,
spl155_383,
inference(avatar_split_clause,[],[f2707,f8131]) ).
thf(f8131,plain,
( spl155_383
<=> ! [X0: nat,X1: nat] :
( ( X0 != X1 )
| ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),nil_Pr1308055047at_nat),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_383])]) ).
thf(f2707,plain,
! [X0: nat,X1: nat] :
( ( X0 != X1 )
| ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),nil_Pr1308055047at_nat),X1) ) ),
inference(equality_proxy_clausification,[],[f2706]) ).
thf(f2706,plain,
! [X0: nat,X1: nat] :
( ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) )
| ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),nil_Pr1308055047at_nat),X1) ) ),
inference(binary_proxy_clausification,[],[f1706]) ).
thf(f8129,plain,
( spl155_382
| ~ spl155_340
| ~ spl155_370 ),
inference(avatar_split_clause,[],[f7829,f7694,f7415,f8127]) ).
thf(f7415,plain,
( spl155_340
<=> ! [X0: product_prod_nat_nat,X1: product_prod_nat_nat > $o] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X1)) )
| ( $false = vAPP(product_prod_nat_nat,$o,X1,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_340])]) ).
thf(f7829,plain,
( ! [X0: product_prod_nat_nat > $o] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X0)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p))) )
| ( $false = vAPP(product_prod_nat_nat,$o,X0,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)) ) )
| ~ spl155_340
| ~ spl155_370 ),
inference(trivial_inequality_removal,[],[f7826]) ).
thf(f7826,plain,
( ! [X0: product_prod_nat_nat > $o] :
( ( $true != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X0)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p))) )
| ( $false = vAPP(product_prod_nat_nat,$o,X0,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)) ) )
| ~ spl155_340
| ~ spl155_370 ),
inference(superposition,[],[f7695,f7416]) ).
thf(f7416,plain,
( ! [X0: product_prod_nat_nat,X1: product_prod_nat_nat > $o] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X1)) )
| ( $false = vAPP(product_prod_nat_nat,$o,X1,X0) ) )
| ~ spl155_340 ),
inference(avatar_component_clause,[],[f7415]) ).
thf(f8121,plain,
( spl155_381
| ~ spl155_246
| ~ spl155_247 ),
inference(avatar_split_clause,[],[f6146,f6142,f6132,f8119]) ).
thf(f8119,plain,
( spl155_381
<=> ! [X0: nat] : ( vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),adjacent_nodes_a,c),X0) = vAPP(list_nat,set_nat,set_nat2,vAPP(set_nat,list_nat,sK8,vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),adjacent_nodes_a,c),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_381])]) ).
thf(f6146,plain,
( ! [X0: nat] : ( vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),adjacent_nodes_a,c),X0) = vAPP(list_nat,set_nat,set_nat2,vAPP(set_nat,list_nat,sK8,vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),adjacent_nodes_a,c),X0))) )
| ~ spl155_246
| ~ spl155_247 ),
inference(trivial_inequality_removal,[],[f6145]) ).
thf(f6145,plain,
( ! [X0: nat] :
( ( $true != $true )
| ( vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),adjacent_nodes_a,c),X0) = vAPP(list_nat,set_nat,set_nat2,vAPP(set_nat,list_nat,sK8,vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),adjacent_nodes_a,c),X0))) ) )
| ~ spl155_246
| ~ spl155_247 ),
inference(superposition,[],[f6133,f6143]) ).
thf(f7997,plain,
( spl155_380
| ~ spl155_87
| ~ spl155_94 ),
inference(avatar_split_clause,[],[f3414,f3394,f3293,f7995]) ).
thf(f7995,plain,
( spl155_380
<=> ! [X0: set_Pr1986765409at_nat,X1: nat] :
( ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X1),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0)) )
| ( $true = vAPP(nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(nat,$o),sP1,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_380])]) ).
thf(f3414,plain,
( ! [X0: set_Pr1986765409at_nat,X1: nat] :
( ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X1),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0)) )
| ( $true = vAPP(nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(nat,$o),sP1,X0),X1) ) )
| ~ spl155_87
| ~ spl155_94 ),
inference(trivial_inequality_removal,[],[f3409]) ).
thf(f3409,plain,
( ! [X0: set_Pr1986765409at_nat,X1: nat] :
( ( $true != $true )
| ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X1),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0)) )
| ( $true = vAPP(nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(nat,$o),sP1,X0),X1) ) )
| ~ spl155_87
| ~ spl155_94 ),
inference(superposition,[],[f3294,f3395]) ).
thf(f7993,plain,
( spl155_379
| ~ spl155_86
| ~ spl155_94 ),
inference(avatar_split_clause,[],[f3413,f3394,f3289,f7991]) ).
thf(f7991,plain,
( spl155_379
<=> ! [X0: set_Pr1986765409at_nat,X1: nat] :
( ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0)),X1) )
| ( $true = vAPP(nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(nat,$o),sP1,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_379])]) ).
thf(f3413,plain,
( ! [X0: set_Pr1986765409at_nat,X1: nat] :
( ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0)),X1) )
| ( $true = vAPP(nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(nat,$o),sP1,X0),X1) ) )
| ~ spl155_86
| ~ spl155_94 ),
inference(trivial_inequality_removal,[],[f3410]) ).
thf(f3410,plain,
( ! [X0: set_Pr1986765409at_nat,X1: nat] :
( ( $true != $true )
| ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0)),X1) )
| ( $true = vAPP(nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(nat,$o),sP1,X0),X1) ) )
| ~ spl155_86
| ~ spl155_94 ),
inference(superposition,[],[f3290,f3395]) ).
thf(f7989,plain,
( spl155_378
| ~ spl155_2
| ~ spl155_370 ),
inference(avatar_split_clause,[],[f7828,f7694,f2739,f7987]) ).
thf(f7828,plain,
( ! [X0: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p))) )
| ( $false = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),X0) ) )
| ~ spl155_2
| ~ spl155_370 ),
inference(trivial_inequality_removal,[],[f7827]) ).
thf(f7827,plain,
( ! [X0: set_Pr1986765409at_nat] :
( ( $true != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p))) )
| ( $false = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),X0) ) )
| ~ spl155_2
| ~ spl155_370 ),
inference(superposition,[],[f7695,f2740]) ).
thf(f7985,plain,
( spl155_377
| ~ spl155_87
| ~ spl155_92 ),
inference(avatar_split_clause,[],[f3407,f3386,f3293,f7983]) ).
thf(f7983,plain,
( spl155_377
<=> ! [X0: set_nat,X1: nat] :
( ( vAPP(set_nat,nat,finite_card_nat,X0) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X1),vAPP(set_nat,nat,finite_card_nat,X0)) )
| ( $true = vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_377])]) ).
thf(f3407,plain,
( ! [X0: set_nat,X1: nat] :
( ( vAPP(set_nat,nat,finite_card_nat,X0) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X1),vAPP(set_nat,nat,finite_card_nat,X0)) )
| ( $true = vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,X0),X1) ) )
| ~ spl155_87
| ~ spl155_92 ),
inference(trivial_inequality_removal,[],[f3402]) ).
thf(f3402,plain,
( ! [X0: set_nat,X1: nat] :
( ( $true != $true )
| ( vAPP(set_nat,nat,finite_card_nat,X0) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X1),vAPP(set_nat,nat,finite_card_nat,X0)) )
| ( $true = vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,X0),X1) ) )
| ~ spl155_87
| ~ spl155_92 ),
inference(superposition,[],[f3294,f3387]) ).
thf(f7981,plain,
( spl155_376
| ~ spl155_86
| ~ spl155_92 ),
inference(avatar_split_clause,[],[f3406,f3386,f3289,f7979]) ).
thf(f7979,plain,
( spl155_376
<=> ! [X0: set_nat,X1: nat] :
( ( vAPP(set_nat,nat,finite_card_nat,X0) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,vAPP(set_nat,nat,finite_card_nat,X0)),X1) )
| ( $true = vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_376])]) ).
thf(f3406,plain,
( ! [X0: set_nat,X1: nat] :
( ( vAPP(set_nat,nat,finite_card_nat,X0) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,vAPP(set_nat,nat,finite_card_nat,X0)),X1) )
| ( $true = vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,X0),X1) ) )
| ~ spl155_86
| ~ spl155_92 ),
inference(trivial_inequality_removal,[],[f3403]) ).
thf(f3403,plain,
( ! [X0: set_nat,X1: nat] :
( ( $true != $true )
| ( vAPP(set_nat,nat,finite_card_nat,X0) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,vAPP(set_nat,nat,finite_card_nat,X0)),X1) )
| ( $true = vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,X0),X1) ) )
| ~ spl155_86
| ~ spl155_92 ),
inference(superposition,[],[f3290,f3387]) ).
thf(f7977,plain,
( spl155_375
| ~ spl155_11
| ~ spl155_12 ),
inference(avatar_split_clause,[],[f2847,f2818,f2814,f7975]) ).
thf(f7975,plain,
( spl155_375
<=> ! [X2: set_Pr1986765409at_nat,X0: nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X2),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sK11,X0),X1))) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_375])]) ).
thf(f2814,plain,
( spl155_11
<=> ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_11])]) ).
thf(f2847,plain,
( ! [X2: set_Pr1986765409at_nat,X0: nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X2),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sK11,X0),X1))) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X1) ) )
| ~ spl155_11
| ~ spl155_12 ),
inference(trivial_inequality_removal,[],[f2842]) ).
thf(f2842,plain,
( ! [X2: set_Pr1986765409at_nat,X0: nat,X1: set_Pr1986765409at_nat] :
( ( $true != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X2),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sK11,X0),X1))) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X1) ) )
| ~ spl155_11
| ~ spl155_12 ),
inference(superposition,[],[f2815,f2819]) ).
thf(f2815,plain,
( ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X1) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1)) ) )
| ~ spl155_11 ),
inference(avatar_component_clause,[],[f2814]) ).
thf(f7973,plain,
( spl155_374
| ~ spl155_10
| ~ spl155_12 ),
inference(avatar_split_clause,[],[f2846,f2818,f2810,f7971]) ).
thf(f7971,plain,
( spl155_374
<=> ! [X2: set_Pr1986765409at_nat,X0: nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sK11,X0),X1)),X2)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_374])]) ).
thf(f2810,plain,
( spl155_10
<=> ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_10])]) ).
thf(f2846,plain,
( ! [X2: set_Pr1986765409at_nat,X0: nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sK11,X0),X1)),X2)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X1) ) )
| ~ spl155_10
| ~ spl155_12 ),
inference(trivial_inequality_removal,[],[f2843]) ).
thf(f2843,plain,
( ! [X2: set_Pr1986765409at_nat,X0: nat,X1: set_Pr1986765409at_nat] :
( ( $true != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sK11,X0),X1)),X2)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X1) ) )
| ~ spl155_10
| ~ spl155_12 ),
inference(superposition,[],[f2811,f2819]) ).
thf(f2811,plain,
( ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1)) ) )
| ~ spl155_10 ),
inference(avatar_component_clause,[],[f2810]) ).
thf(f7708,plain,
( spl155_373
| ~ spl155_76
| ~ spl155_89 ),
inference(avatar_split_clause,[],[f3364,f3301,f3244,f7706]) ).
thf(f7706,plain,
( spl155_373
<=> ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] : ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1) = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_373])]) ).
thf(f3364,plain,
( ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] : ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1) = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1)),X0) )
| ~ spl155_76
| ~ spl155_89 ),
inference(trivial_inequality_removal,[],[f3355]) ).
thf(f3355,plain,
( ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true != $true )
| ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1) = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1)),X0) ) )
| ~ spl155_76
| ~ spl155_89 ),
inference(superposition,[],[f3302,f3245]) ).
thf(f7704,plain,
( spl155_372
| ~ spl155_77
| ~ spl155_89 ),
inference(avatar_split_clause,[],[f3363,f3301,f3248,f7702]) ).
thf(f7702,plain,
( spl155_372
<=> ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] : ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1) = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_372])]) ).
thf(f3363,plain,
( ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] : ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1) = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1)),X1) )
| ~ spl155_77
| ~ spl155_89 ),
inference(trivial_inequality_removal,[],[f3356]) ).
thf(f3356,plain,
( ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true != $true )
| ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1) = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1)),X1) ) )
| ~ spl155_77
| ~ spl155_89 ),
inference(superposition,[],[f3302,f3249]) ).
thf(f7700,plain,
( spl155_371
| ~ spl155_76
| ~ spl155_88 ),
inference(avatar_split_clause,[],[f3352,f3297,f3244,f7698]) ).
thf(f7698,plain,
( spl155_371
<=> ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] : ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1) = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_371])]) ).
thf(f3352,plain,
( ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] : ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1) = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1)) )
| ~ spl155_76
| ~ spl155_88 ),
inference(trivial_inequality_removal,[],[f3343]) ).
thf(f3343,plain,
( ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true != $true )
| ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1) = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1)) ) )
| ~ spl155_76
| ~ spl155_88 ),
inference(superposition,[],[f3298,f3245]) ).
thf(f7696,plain,
( spl155_370
| ~ spl155_33
| ~ spl155_354 ),
inference(avatar_split_clause,[],[f7647,f7593,f2977,f7694]) ).
thf(f7647,plain,
( ! [X0: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p))) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),X0) ) )
| ~ spl155_33
| ~ spl155_354 ),
inference(trivial_inequality_removal,[],[f7646]) ).
thf(f7646,plain,
( ! [X0: set_Pr1986765409at_nat] :
( ( $true != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p))) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),X0) ) )
| ~ spl155_33
| ~ spl155_354 ),
inference(superposition,[],[f2978,f7595]) ).
thf(f7692,plain,
( spl155_369
| ~ spl155_77
| ~ spl155_88 ),
inference(avatar_split_clause,[],[f3351,f3297,f3248,f7690]) ).
thf(f7690,plain,
( spl155_369
<=> ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] : ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1) = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_369])]) ).
thf(f3351,plain,
( ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] : ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1) = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1)) )
| ~ spl155_77
| ~ spl155_88 ),
inference(trivial_inequality_removal,[],[f3344]) ).
thf(f3344,plain,
( ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true != $true )
| ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1) = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1)) ) )
| ~ spl155_77
| ~ spl155_88 ),
inference(superposition,[],[f3298,f3249]) ).
thf(f7688,plain,
( spl155_368
| ~ spl155_75
| ~ spl155_87 ),
inference(avatar_split_clause,[],[f3340,f3293,f3240,f7686]) ).
thf(f7686,plain,
( spl155_368
<=> ! [X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_368])]) ).
thf(f3340,plain,
( ! [X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X1)) )
| ~ spl155_75
| ~ spl155_87 ),
inference(trivial_inequality_removal,[],[f3335]) ).
thf(f3335,plain,
( ! [X0: nat,X1: nat] :
( ( $true != $true )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X1)) ) )
| ~ spl155_75
| ~ spl155_87 ),
inference(superposition,[],[f3294,f3241]) ).
thf(f7684,plain,
( spl155_367
| ~ spl155_74
| ~ spl155_87 ),
inference(avatar_split_clause,[],[f3339,f3293,f3236,f7682]) ).
thf(f7682,plain,
( spl155_367
<=> ! [X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_367])]) ).
thf(f3339,plain,
( ! [X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X1)) )
| ~ spl155_74
| ~ spl155_87 ),
inference(trivial_inequality_removal,[],[f3336]) ).
thf(f3336,plain,
( ! [X0: nat,X1: nat] :
( ( $true != $true )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X1)) ) )
| ~ spl155_74
| ~ spl155_87 ),
inference(superposition,[],[f3294,f3237]) ).
thf(f7680,plain,
( spl155_366
| ~ spl155_75
| ~ spl155_86 ),
inference(avatar_split_clause,[],[f3332,f3289,f3240,f7678]) ).
thf(f7678,plain,
( spl155_366
<=> ! [X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X1)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_366])]) ).
thf(f3332,plain,
( ! [X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X1)),X0) )
| ~ spl155_75
| ~ spl155_86 ),
inference(trivial_inequality_removal,[],[f3327]) ).
thf(f3327,plain,
( ! [X0: nat,X1: nat] :
( ( $true != $true )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X1)),X0) ) )
| ~ spl155_75
| ~ spl155_86 ),
inference(superposition,[],[f3290,f3241]) ).
thf(f7676,plain,
( spl155_365
| ~ spl155_74
| ~ spl155_86 ),
inference(avatar_split_clause,[],[f3331,f3289,f3236,f7674]) ).
thf(f7674,plain,
( spl155_365
<=> ! [X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_365])]) ).
thf(f3331,plain,
( ! [X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X1)),X1) )
| ~ spl155_74
| ~ spl155_86 ),
inference(trivial_inequality_removal,[],[f3328]) ).
thf(f3328,plain,
( ! [X0: nat,X1: nat] :
( ( $true != $true )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X1)),X1) ) )
| ~ spl155_74
| ~ spl155_86 ),
inference(superposition,[],[f3290,f3237]) ).
thf(f7672,plain,
( spl155_364
| ~ spl155_73
| ~ spl155_85 ),
inference(avatar_split_clause,[],[f3324,f3285,f3232,f7670]) ).
thf(f7670,plain,
( spl155_364
<=> ! [X0: set_nat,X1: set_nat] : ( vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X1) = vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X1)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_364])]) ).
thf(f3324,plain,
( ! [X0: set_nat,X1: set_nat] : ( vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X1) = vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X1)),X0) )
| ~ spl155_73
| ~ spl155_85 ),
inference(trivial_inequality_removal,[],[f3319]) ).
thf(f3319,plain,
( ! [X0: set_nat,X1: set_nat] :
( ( $true != $true )
| ( vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X1) = vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X1)),X0) ) )
| ~ spl155_73
| ~ spl155_85 ),
inference(superposition,[],[f3286,f3233]) ).
thf(f7668,plain,
( spl155_363
| ~ spl155_72
| ~ spl155_85 ),
inference(avatar_split_clause,[],[f3323,f3285,f3228,f7666]) ).
thf(f7666,plain,
( spl155_363
<=> ! [X0: set_nat,X1: set_nat] : ( vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X1) = vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_363])]) ).
thf(f3323,plain,
( ! [X0: set_nat,X1: set_nat] : ( vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X1) = vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X1)),X1) )
| ~ spl155_72
| ~ spl155_85 ),
inference(trivial_inequality_removal,[],[f3320]) ).
thf(f3320,plain,
( ! [X0: set_nat,X1: set_nat] :
( ( $true != $true )
| ( vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X1) = vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X1)),X1) ) )
| ~ spl155_72
| ~ spl155_85 ),
inference(superposition,[],[f3286,f3229]) ).
thf(f7664,plain,
( spl155_362
| ~ spl155_73
| ~ spl155_84 ),
inference(avatar_split_clause,[],[f3316,f3281,f3232,f7662]) ).
thf(f7662,plain,
( spl155_362
<=> ! [X0: set_nat,X1: set_nat] : ( vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X1) = vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_362])]) ).
thf(f3316,plain,
( ! [X0: set_nat,X1: set_nat] : ( vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X1) = vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X1)) )
| ~ spl155_73
| ~ spl155_84 ),
inference(trivial_inequality_removal,[],[f3311]) ).
thf(f3311,plain,
( ! [X0: set_nat,X1: set_nat] :
( ( $true != $true )
| ( vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X1) = vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X1)) ) )
| ~ spl155_73
| ~ spl155_84 ),
inference(superposition,[],[f3282,f3233]) ).
thf(f7660,plain,
( spl155_361
| ~ spl155_72
| ~ spl155_84 ),
inference(avatar_split_clause,[],[f3315,f3281,f3228,f7658]) ).
thf(f7658,plain,
( spl155_361
<=> ! [X0: set_nat,X1: set_nat] : ( vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X1) = vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_361])]) ).
thf(f3315,plain,
( ! [X0: set_nat,X1: set_nat] : ( vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X1) = vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X1)) )
| ~ spl155_72
| ~ spl155_84 ),
inference(trivial_inequality_removal,[],[f3312]) ).
thf(f3312,plain,
( ! [X0: set_nat,X1: set_nat] :
( ( $true != $true )
| ( vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X1) = vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X1)) ) )
| ~ spl155_72
| ~ spl155_84 ),
inference(superposition,[],[f3282,f3229]) ).
thf(f7656,plain,
( spl155_360
| ~ spl155_19
| ~ spl155_39 ),
inference(avatar_split_clause,[],[f3021,f3015,f2882,f7653]) ).
thf(f3021,plain,
( ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),s),p),t) )
| ~ spl155_19
| ~ spl155_39 ),
inference(trivial_inequality_removal,[],[f3018]) ).
thf(f3018,plain,
( ( $true != $true )
| ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),s),p),t) )
| ~ spl155_19
| ~ spl155_39 ),
inference(superposition,[],[f3016,f2884]) ).
thf(f7616,plain,
( spl155_359
| ~ spl155_248
| ~ spl155_250 ),
inference(avatar_split_clause,[],[f6183,f6171,f6148,f7614]) ).
thf(f7614,plain,
( spl155_359
<=> ! [X0: product_prod_nat_nat > a,X1: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) )
| ( $true = vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0)),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_359])]) ).
thf(f6183,plain,
( ! [X0: product_prod_nat_nat > a,X1: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) )
| ( $true = vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0)),X1) ) )
| ~ spl155_248
| ~ spl155_250 ),
inference(trivial_inequality_removal,[],[f6180]) ).
thf(f6180,plain,
( ! [X0: product_prod_nat_nat > a,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) )
| ( $true = vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0)),X1) ) )
| ~ spl155_248
| ~ spl155_250 ),
inference(superposition,[],[f6172,f6149]) ).
thf(f7612,plain,
( spl155_358
| ~ spl155_90
| ~ spl155_99 ),
inference(avatar_split_clause,[],[f3470,f3432,f3367,f7610]) ).
thf(f7610,plain,
( spl155_358
<=> ! [X0: product_prod_nat_nat > a,X1: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),outgoing_a,X0),X1)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_358])]) ).
thf(f3470,plain,
( ! [X0: product_prod_nat_nat > a,X1: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),outgoing_a,X0),X1)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) ) )
| ~ spl155_90
| ~ spl155_99 ),
inference(trivial_inequality_removal,[],[f3465]) ).
thf(f3465,plain,
( ! [X0: product_prod_nat_nat > a,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),outgoing_a,X0),X1)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) ) )
| ~ spl155_90
| ~ spl155_99 ),
inference(superposition,[],[f3368,f3433]) ).
thf(f7608,plain,
( spl155_357
| ~ spl155_90
| ~ spl155_98 ),
inference(avatar_split_clause,[],[f3464,f3428,f3367,f7606]) ).
thf(f7606,plain,
( spl155_357
<=> ! [X0: product_prod_nat_nat > a,X1: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),incoming_a,X0),X1)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_357])]) ).
thf(f3464,plain,
( ! [X0: product_prod_nat_nat > a,X1: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),incoming_a,X0),X1)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) ) )
| ~ spl155_90
| ~ spl155_98 ),
inference(trivial_inequality_removal,[],[f3459]) ).
thf(f3459,plain,
( ! [X0: product_prod_nat_nat > a,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),incoming_a,X0),X1)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) ) )
| ~ spl155_90
| ~ spl155_98 ),
inference(superposition,[],[f3368,f3429]) ).
thf(f7604,plain,
( spl155_356
| ~ spl155_90
| ~ spl155_97 ),
inference(avatar_split_clause,[],[f3458,f3424,f3367,f7602]) ).
thf(f7602,plain,
( spl155_356
<=> ! [X0: product_prod_nat_nat > a,X1: set_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),outgoing_a2,X0),X1)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_356])]) ).
thf(f3458,plain,
( ! [X0: product_prod_nat_nat > a,X1: set_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),outgoing_a2,X0),X1)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) ) )
| ~ spl155_90
| ~ spl155_97 ),
inference(trivial_inequality_removal,[],[f3453]) ).
thf(f3453,plain,
( ! [X0: product_prod_nat_nat > a,X1: set_nat] :
( ( $true != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),outgoing_a2,X0),X1)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) ) )
| ~ spl155_90
| ~ spl155_97 ),
inference(superposition,[],[f3368,f3425]) ).
thf(f7600,plain,
( spl155_355
| ~ spl155_90
| ~ spl155_96 ),
inference(avatar_split_clause,[],[f3452,f3420,f3367,f7598]) ).
thf(f7598,plain,
( spl155_355
<=> ! [X0: product_prod_nat_nat > a,X1: set_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),incoming_a2,X0),X1)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_355])]) ).
thf(f3452,plain,
( ! [X0: product_prod_nat_nat > a,X1: set_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),incoming_a2,X0),X1)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) ) )
| ~ spl155_90
| ~ spl155_96 ),
inference(trivial_inequality_removal,[],[f3447]) ).
thf(f3447,plain,
( ! [X0: product_prod_nat_nat > a,X1: set_nat] :
( ( $true != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),incoming_a2,X0),X1)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) ) )
| ~ spl155_90
| ~ spl155_96 ),
inference(superposition,[],[f3368,f3421]) ).
thf(f7596,plain,
( spl155_354
| ~ spl155_125
| ~ spl155_349 ),
inference(avatar_split_clause,[],[f7527,f7504,f3763,f7593]) ).
thf(f7527,plain,
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p)) )
| ~ spl155_125
| ~ spl155_349 ),
inference(trivial_inequality_removal,[],[f7523]) ).
thf(f7523,plain,
( ( $true != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p)) )
| ~ spl155_125
| ~ spl155_349 ),
inference(superposition,[],[f7505,f3765]) ).
thf(f7545,plain,
( spl155_353
| ~ spl155_75
| ~ spl155_104 ),
inference(avatar_split_clause,[],[f3580,f3484,f3240,f7543]) ).
thf(f7543,plain,
( spl155_353
<=> ! [X0: set_Pr1986765409at_nat,X1: nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK28,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0)),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_353])]) ).
thf(f3580,plain,
( ! [X0: set_Pr1986765409at_nat,X1: nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK28,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0)),X1))) )
| ~ spl155_75
| ~ spl155_104 ),
inference(trivial_inequality_removal,[],[f3571]) ).
thf(f3571,plain,
( ! [X0: set_Pr1986765409at_nat,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK28,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0)),X1))) ) )
| ~ spl155_75
| ~ spl155_104 ),
inference(superposition,[],[f3485,f3241]) ).
thf(f7541,plain,
( spl155_352
| ~ spl155_74
| ~ spl155_104 ),
inference(avatar_split_clause,[],[f3579,f3484,f3236,f7539]) ).
thf(f7539,plain,
( spl155_352
<=> ! [X0: nat,X1: set_Pr1986765409at_nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK28,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_352])]) ).
thf(f3579,plain,
( ! [X0: nat,X1: set_Pr1986765409at_nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK28,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)))) )
| ~ spl155_74
| ~ spl155_104 ),
inference(trivial_inequality_removal,[],[f3572]) ).
thf(f3572,plain,
( ! [X0: nat,X1: set_Pr1986765409at_nat] :
( ( $true != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK28,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)))) ) )
| ~ spl155_74
| ~ spl155_104 ),
inference(superposition,[],[f3485,f3237]) ).
thf(f7537,plain,
( spl155_351
| ~ spl155_79
| ~ spl155_89 ),
inference(avatar_split_clause,[],[f3361,f3301,f3260,f7534]) ).
thf(f7534,plain,
( spl155_351
<=> ( vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c) = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,c)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_351])]) ).
thf(f3361,plain,
( ( vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c) = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,c)) )
| ~ spl155_79
| ~ spl155_89 ),
inference(trivial_inequality_removal,[],[f3358]) ).
thf(f3358,plain,
( ( $true != $true )
| ( vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c) = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,c)) )
| ~ spl155_79
| ~ spl155_89 ),
inference(superposition,[],[f3302,f3262]) ).
thf(f7532,plain,
( spl155_350
| ~ spl155_79
| ~ spl155_88 ),
inference(avatar_split_clause,[],[f3349,f3297,f3260,f7529]) ).
thf(f7529,plain,
( spl155_350
<=> ( vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c) = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,c)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_350])]) ).
thf(f3349,plain,
( ( vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c) = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,c)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) )
| ~ spl155_79
| ~ spl155_88 ),
inference(trivial_inequality_removal,[],[f3346]) ).
thf(f3346,plain,
( ( $true != $true )
| ( vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c) = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,c)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) )
| ~ spl155_79
| ~ spl155_88 ),
inference(superposition,[],[f3298,f3262]) ).
thf(f7506,plain,
( spl155_349
| ~ spl155_71
| ~ spl155_122 ),
inference(avatar_split_clause,[],[f3743,f3702,f3223,f7504]) ).
thf(f3743,plain,
( ! [X0: product_prod_nat_nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),edges) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p)) ) )
| ~ spl155_71
| ~ spl155_122 ),
inference(trivial_inequality_removal,[],[f3730]) ).
thf(f3730,plain,
( ! [X0: product_prod_nat_nat] :
( ( $true != $true )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),edges) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p)) ) )
| ~ spl155_71
| ~ spl155_122 ),
inference(superposition,[],[f3703,f3225]) ).
thf(f7502,plain,
( spl155_348
| ~ spl155_2
| ~ spl155_17 ),
inference(avatar_split_clause,[],[f2875,f2868,f2739,f7500]) ).
thf(f7500,plain,
( spl155_348
<=> ! [X0: set_Pr1986765409at_nat,X1: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK17,X0),X1)) )
| ( $false = vAPP(nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(nat,$o),sP1,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_348])]) ).
thf(f2868,plain,
( spl155_17
<=> ! [X0: nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK17,X1),X0)) )
| ( $true != vAPP(nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(nat,$o),sP1,X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_17])]) ).
thf(f2875,plain,
( ! [X0: set_Pr1986765409at_nat,X1: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK17,X0),X1)) )
| ( $false = vAPP(nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(nat,$o),sP1,X0),X1) ) )
| ~ spl155_2
| ~ spl155_17 ),
inference(trivial_inequality_removal,[],[f2874]) ).
thf(f2874,plain,
( ! [X0: set_Pr1986765409at_nat,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK17,X0),X1)) )
| ( $false = vAPP(nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(nat,$o),sP1,X0),X1) ) )
| ~ spl155_2
| ~ spl155_17 ),
inference(superposition,[],[f2869,f2740]) ).
thf(f2869,plain,
( ! [X0: nat,X1: set_Pr1986765409at_nat] :
( ( $true != vAPP(nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(nat,$o),sP1,X1),X0) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK17,X1),X0)) ) )
| ~ spl155_17 ),
inference(avatar_component_clause,[],[f2868]) ).
thf(f7497,plain,
spl155_347,
inference(avatar_split_clause,[],[f2634,f7495]) ).
thf(f7495,plain,
( spl155_347
<=> ! [X0: product_prod_nat_nat,X3: list_P559422087at_nat,X2: product_prod_nat_nat,X1: list_P559422087at_nat] :
( ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,X0),X1) = vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,X2),X3) )
| ( X1 != X3 )
| ( X0 != X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_347])]) ).
thf(f2634,plain,
! [X2: product_prod_nat_nat,X3: list_P559422087at_nat,X0: product_prod_nat_nat,X1: list_P559422087at_nat] :
( ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,X0),X1) = vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,X2),X3) )
| ( X1 != X3 )
| ( X0 != X2 ) ),
inference(equality_proxy_clausification,[],[f2633]) ).
thf(f2633,plain,
! [X2: product_prod_nat_nat,X3: list_P559422087at_nat,X0: product_prod_nat_nat,X1: list_P559422087at_nat] :
( ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,X0),X1) = vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,X2),X3) )
| ( X1 != X3 )
| ( $false = vAPP(product_prod_nat_nat,$o,vAPP(product_prod_nat_nat,sTfun(product_prod_nat_nat,$o),vEQ(product_prod_nat_nat),X0),X2) ) ),
inference(equality_proxy_clausification,[],[f2632]) ).
thf(f2632,plain,
! [X2: product_prod_nat_nat,X3: list_P559422087at_nat,X0: product_prod_nat_nat,X1: list_P559422087at_nat] :
( ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,X0),X1) = vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,X2),X3) )
| ( $false = vAPP(list_P559422087at_nat,$o,vAPP(list_P559422087at_nat,sTfun(list_P559422087at_nat,$o),vEQ(list_P559422087at_nat),X1),X3) )
| ( $false = vAPP(product_prod_nat_nat,$o,vAPP(product_prod_nat_nat,sTfun(product_prod_nat_nat,$o),vEQ(product_prod_nat_nat),X0),X2) ) ),
inference(binary_proxy_clausification,[],[f2631]) ).
thf(f2631,plain,
! [X2: product_prod_nat_nat,X3: list_P559422087at_nat,X0: product_prod_nat_nat,X1: list_P559422087at_nat] :
( ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,X0),X1) = vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,X2),X3) )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(product_prod_nat_nat,$o,vAPP(product_prod_nat_nat,sTfun(product_prod_nat_nat,$o),vEQ(product_prod_nat_nat),X0),X2)),vAPP(list_P559422087at_nat,$o,vAPP(list_P559422087at_nat,sTfun(list_P559422087at_nat,$o),vEQ(list_P559422087at_nat),X1),X3)) ) ),
inference(equality_proxy_clausification,[],[f2624]) ).
thf(f2624,plain,
! [X2: product_prod_nat_nat,X3: list_P559422087at_nat,X0: product_prod_nat_nat,X1: list_P559422087at_nat] :
( ( $true = vAPP(list_P559422087at_nat,$o,vAPP(list_P559422087at_nat,sTfun(list_P559422087at_nat,$o),vEQ(list_P559422087at_nat),vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,X0),X1)),vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,X2),X3)) )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(product_prod_nat_nat,$o,vAPP(product_prod_nat_nat,sTfun(product_prod_nat_nat,$o),vEQ(product_prod_nat_nat),X0),X2)),vAPP(list_P559422087at_nat,$o,vAPP(list_P559422087at_nat,sTfun(list_P559422087at_nat,$o),vEQ(list_P559422087at_nat),X1),X3)) ) ),
inference(binary_proxy_clausification,[],[f1985]) ).
thf(f1985,plain,
! [X2: product_prod_nat_nat,X3: list_P559422087at_nat,X0: product_prod_nat_nat,X1: list_P559422087at_nat] : ( vAPP(list_P559422087at_nat,$o,vAPP(list_P559422087at_nat,sTfun(list_P559422087at_nat,$o),vEQ(list_P559422087at_nat),vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,X0),X1)),vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,X2),X3)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(product_prod_nat_nat,$o,vAPP(product_prod_nat_nat,sTfun(product_prod_nat_nat,$o),vEQ(product_prod_nat_nat),X0),X2)),vAPP(list_P559422087at_nat,$o,vAPP(list_P559422087at_nat,sTfun(list_P559422087at_nat,$o),vEQ(list_P559422087at_nat),X1),X3)) ),
inference(cnf_transformation,[],[f899]) ).
thf(f899,plain,
! [X0: product_prod_nat_nat,X1: list_P559422087at_nat,X2: product_prod_nat_nat,X3: list_P559422087at_nat] : ( vAPP(list_P559422087at_nat,$o,vAPP(list_P559422087at_nat,sTfun(list_P559422087at_nat,$o),vEQ(list_P559422087at_nat),vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,X0),X1)),vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,X2),X3)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(product_prod_nat_nat,$o,vAPP(product_prod_nat_nat,sTfun(product_prod_nat_nat,$o),vEQ(product_prod_nat_nat),X0),X2)),vAPP(list_P559422087at_nat,$o,vAPP(list_P559422087at_nat,sTfun(list_P559422087at_nat,$o),vEQ(list_P559422087at_nat),X1),X3)) ),
inference(fool_elimination,[],[f898]) ).
thf(f898,plain,
! [X0: product_prod_nat_nat,X1: list_P559422087at_nat,X2: product_prod_nat_nat,X3: list_P559422087at_nat] :
( ( ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,X0),X1) = vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,X2),X3) )
= ( X1 = X3 ) )
& ( X0 = X2 ) ),
inference(rectify,[],[f342]) ).
thf(f342,axiom,
! [X53: product_prod_nat_nat,X54: list_P559422087at_nat,X55: product_prod_nat_nat,X56: list_P559422087at_nat] :
( ( ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,X53),X54) = vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,X55),X56) )
= ( X54 = X56 ) )
& ( X53 = X55 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_341_list_Oinject) ).
thf(f7486,plain,
( spl155_346
| ~ spl155_246
| ~ spl155_249 ),
inference(avatar_split_clause,[],[f6169,f6162,f6132,f7484]) ).
thf(f7484,plain,
( spl155_346
<=> ! [X0: set_nat,X1: nat] :
( ( vAPP(list_nat,set_nat,set_nat2,vAPP(set_nat,list_nat,sK8,X0)) = X0 )
| ( vAPP(set_nat,nat,finite_card_nat,vAPP(set_nat,set_nat,vAPP(nat,sTfun(set_nat,set_nat),sK10,X1),X0)) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_346])]) ).
thf(f6169,plain,
( ! [X0: set_nat,X1: nat] :
( ( vAPP(list_nat,set_nat,set_nat2,vAPP(set_nat,list_nat,sK8,X0)) = X0 )
| ( vAPP(set_nat,nat,finite_card_nat,vAPP(set_nat,set_nat,vAPP(nat,sTfun(set_nat,set_nat),sK10,X1),X0)) = X1 ) )
| ~ spl155_246
| ~ spl155_249 ),
inference(trivial_inequality_removal,[],[f6168]) ).
thf(f6168,plain,
( ! [X0: set_nat,X1: nat] :
( ( $true != $true )
| ( vAPP(list_nat,set_nat,set_nat2,vAPP(set_nat,list_nat,sK8,X0)) = X0 )
| ( vAPP(set_nat,nat,finite_card_nat,vAPP(set_nat,set_nat,vAPP(nat,sTfun(set_nat,set_nat),sK10,X1),X0)) = X1 ) )
| ~ spl155_246
| ~ spl155_249 ),
inference(superposition,[],[f6133,f6163]) ).
thf(f7476,plain,
( spl155_345
| ~ spl155_258
| ~ spl155_272 ),
inference(avatar_split_clause,[],[f6394,f6388,f6257,f7474]) ).
thf(f7474,plain,
( spl155_345
<=> ! [X0: nat,X1: nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,c),X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_345])]) ).
thf(f6388,plain,
( spl155_272
<=> ! [X2: nat,X0: product_prod_nat_nat > a,X1: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,X0),X1),X2)) )
| ( $true != vAPP(sTfun(product_prod_nat_nat,a),$o,vAPP(sTfun(sTfun(product_prod_nat_nat,a),set_nat),sTfun(sTfun(product_prod_nat_nat,a),$o),vAPP(sTfun(set_nat,$o),sTfun(sTfun(sTfun(product_prod_nat_nat,a),set_nat),sTfun(sTfun(product_prod_nat_nat,a),$o)),bCOMB,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB)))))),v_a),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_272])]) ).
thf(f6394,plain,
( ! [X0: nat,X1: nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,c),X0),X1)) )
| ~ spl155_258
| ~ spl155_272 ),
inference(trivial_inequality_removal,[],[f6391]) ).
thf(f6391,plain,
( ! [X0: nat,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,c),X0),X1)) ) )
| ~ spl155_258
| ~ spl155_272 ),
inference(superposition,[],[f6389,f6259]) ).
thf(f6389,plain,
( ! [X2: nat,X0: product_prod_nat_nat > a,X1: nat] :
( ( $true != vAPP(sTfun(product_prod_nat_nat,a),$o,vAPP(sTfun(sTfun(product_prod_nat_nat,a),set_nat),sTfun(sTfun(product_prod_nat_nat,a),$o),vAPP(sTfun(set_nat,$o),sTfun(sTfun(sTfun(product_prod_nat_nat,a),set_nat),sTfun(sTfun(product_prod_nat_nat,a),$o)),bCOMB,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB)))))),v_a),X0) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,X0),X1),X2)) ) )
| ~ spl155_272 ),
inference(avatar_component_clause,[],[f6388]) ).
thf(f7454,plain,
( spl155_344
| ~ spl155_181
| ~ spl155_340 ),
inference(avatar_split_clause,[],[f7435,f7415,f4909,f7452]) ).
thf(f7435,plain,
( ! [X0: product_prod_nat_nat > $o] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X0)),edges)) )
| ( $false = vAPP(product_prod_nat_nat,$o,X0,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)) ) )
| ~ spl155_181
| ~ spl155_340 ),
inference(trivial_inequality_removal,[],[f7432]) ).
thf(f7432,plain,
( ! [X0: product_prod_nat_nat > $o] :
( ( $true != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X0)),edges)) )
| ( $false = vAPP(product_prod_nat_nat,$o,X0,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)) ) )
| ~ spl155_181
| ~ spl155_340 ),
inference(superposition,[],[f4910,f7416]) ).
thf(f7429,plain,
spl155_343,
inference(avatar_split_clause,[],[f2728,f7427]) ).
thf(f7427,plain,
( spl155_343
<=> ! [X0: nat,X1: nat > $o] :
( ( $false = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(sTfun(nat,$o),set_nat,collect_nat,X1)) )
| ( $true = vAPP(nat,$o,X1,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_343])]) ).
thf(f2728,plain,
! [X0: nat,X1: nat > $o] :
( ( $false = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(sTfun(nat,$o),set_nat,collect_nat,X1)) )
| ( $true = vAPP(nat,$o,X1,X0) ) ),
inference(binary_proxy_clausification,[],[f1700]) ).
thf(f1700,plain,
! [X0: nat,X1: nat > $o] : ( vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(sTfun(nat,$o),set_nat,collect_nat,X1)) = vAPP(nat,$o,X1,X0) ),
inference(cnf_transformation,[],[f1037]) ).
thf(f1037,plain,
! [X0: nat,X1: nat > $o] : ( vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(sTfun(nat,$o),set_nat,collect_nat,X1)) = vAPP(nat,$o,X1,X0) ),
inference(rectify,[],[f102]) ).
thf(f102,axiom,
! [X13: nat,X18: nat > $o] : ( vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X13),vAPP(sTfun(nat,$o),set_nat,collect_nat,X18)) = vAPP(nat,$o,X18,X13) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_mem__Collect__eq) ).
thf(f7425,plain,
spl155_342,
inference(avatar_split_clause,[],[f2727,f7423]) ).
thf(f7423,plain,
( spl155_342
<=> ! [X0: nat,X1: nat > $o] :
( ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(sTfun(nat,$o),set_nat,collect_nat,X1)) )
| ( $false = vAPP(nat,$o,X1,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_342])]) ).
thf(f2727,plain,
! [X0: nat,X1: nat > $o] :
( ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(sTfun(nat,$o),set_nat,collect_nat,X1)) )
| ( $false = vAPP(nat,$o,X1,X0) ) ),
inference(binary_proxy_clausification,[],[f1700]) ).
thf(f7421,plain,
spl155_341,
inference(avatar_split_clause,[],[f2726,f7419]) ).
thf(f2726,plain,
! [X0: product_prod_nat_nat,X1: product_prod_nat_nat > $o] :
( ( $false = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X1)) )
| ( $true = vAPP(product_prod_nat_nat,$o,X1,X0) ) ),
inference(binary_proxy_clausification,[],[f1701]) ).
thf(f1701,plain,
! [X0: product_prod_nat_nat,X1: product_prod_nat_nat > $o] : ( vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X1)) = vAPP(product_prod_nat_nat,$o,X1,X0) ),
inference(cnf_transformation,[],[f1038]) ).
thf(f1038,plain,
! [X0: product_prod_nat_nat,X1: product_prod_nat_nat > $o] : ( vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X1)) = vAPP(product_prod_nat_nat,$o,X1,X0) ),
inference(rectify,[],[f103]) ).
thf(f103,axiom,
! [X13: product_prod_nat_nat,X18: product_prod_nat_nat > $o] : ( vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X13),vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X18)) = vAPP(product_prod_nat_nat,$o,X18,X13) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_mem__Collect__eq) ).
thf(f7417,plain,
spl155_340,
inference(avatar_split_clause,[],[f2725,f7415]) ).
thf(f2725,plain,
! [X0: product_prod_nat_nat,X1: product_prod_nat_nat > $o] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X1)) )
| ( $false = vAPP(product_prod_nat_nat,$o,X1,X0) ) ),
inference(binary_proxy_clausification,[],[f1701]) ).
thf(f7392,plain,
( spl155_339
| ~ spl155_68
| ~ spl155_105 ),
inference(avatar_split_clause,[],[f3594,f3488,f3209,f7390]) ).
thf(f7390,plain,
( spl155_339
<=> ! [X0: set_Pr1986765409at_nat] : ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0) = vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK28,X0),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_339])]) ).
thf(f3594,plain,
( ! [X0: set_Pr1986765409at_nat] : ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0) = vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK28,X0),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0))) )
| ~ spl155_68
| ~ spl155_105 ),
inference(trivial_inequality_removal,[],[f3583]) ).
thf(f3583,plain,
( ! [X0: set_Pr1986765409at_nat] :
( ( $true != $true )
| ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0) = vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK28,X0),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0))) ) )
| ~ spl155_68
| ~ spl155_105 ),
inference(superposition,[],[f3489,f3210]) ).
thf(f7388,plain,
( spl155_338
| ~ spl155_68
| ~ spl155_103 ),
inference(avatar_split_clause,[],[f3562,f3480,f3209,f7386]) ).
thf(f7386,plain,
( spl155_338
<=> ! [X0: set_nat] : ( vAPP(set_nat,nat,finite_card_nat,X0) = vAPP(set_nat,nat,finite_card_nat,vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK27,X0),vAPP(set_nat,nat,finite_card_nat,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_338])]) ).
thf(f3562,plain,
( ! [X0: set_nat] : ( vAPP(set_nat,nat,finite_card_nat,X0) = vAPP(set_nat,nat,finite_card_nat,vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK27,X0),vAPP(set_nat,nat,finite_card_nat,X0))) )
| ~ spl155_68
| ~ spl155_103 ),
inference(trivial_inequality_removal,[],[f3551]) ).
thf(f3551,plain,
( ! [X0: set_nat] :
( ( $true != $true )
| ( vAPP(set_nat,nat,finite_card_nat,X0) = vAPP(set_nat,nat,finite_card_nat,vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK27,X0),vAPP(set_nat,nat,finite_card_nat,X0))) ) )
| ~ spl155_68
| ~ spl155_103 ),
inference(superposition,[],[f3481,f3210]) ).
thf(f7350,plain,
( spl155_337
| ~ spl155_246
| ~ spl155_248 ),
inference(avatar_split_clause,[],[f6160,f6148,f6132,f7348]) ).
thf(f7348,plain,
( spl155_337
<=> ! [X0: set_nat,X1: nat] :
( ( vAPP(list_nat,set_nat,set_nat2,vAPP(set_nat,list_nat,sK8,X0)) = X0 )
| ( $true = vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_337])]) ).
thf(f6160,plain,
( ! [X0: set_nat,X1: nat] :
( ( vAPP(list_nat,set_nat,set_nat2,vAPP(set_nat,list_nat,sK8,X0)) = X0 )
| ( $true = vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,X0),X1) ) )
| ~ spl155_246
| ~ spl155_248 ),
inference(trivial_inequality_removal,[],[f6151]) ).
thf(f6151,plain,
( ! [X0: set_nat,X1: nat] :
( ( $true != $true )
| ( vAPP(list_nat,set_nat,set_nat2,vAPP(set_nat,list_nat,sK8,X0)) = X0 )
| ( $true = vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,X0),X1) ) )
| ~ spl155_246
| ~ spl155_248 ),
inference(superposition,[],[f6133,f6149]) ).
thf(f7346,plain,
( spl155_336
| ~ spl155_9
| ~ spl155_17 ),
inference(avatar_split_clause,[],[f2876,f2868,f2806,f7344]) ).
thf(f7344,plain,
( spl155_336
<=> ! [X0: set_Pr1986765409at_nat,X1: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK17,X0),X1)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_336])]) ).
thf(f2876,plain,
( ! [X0: set_Pr1986765409at_nat,X1: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK17,X0),X1)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) ) )
| ~ spl155_9
| ~ spl155_17 ),
inference(trivial_inequality_removal,[],[f2873]) ).
thf(f2873,plain,
( ! [X0: set_Pr1986765409at_nat,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK17,X0),X1)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) ) )
| ~ spl155_9
| ~ spl155_17 ),
inference(superposition,[],[f2869,f2807]) ).
thf(f7342,plain,
( spl155_335
| ~ spl155_2
| ~ spl155_11 ),
inference(avatar_split_clause,[],[f2837,f2814,f2739,f7340]) ).
thf(f7340,plain,
( spl155_335
<=> ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),X0)) )
| ( $false = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_335])]) ).
thf(f2837,plain,
( ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),X0)) )
| ( $false = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) ) )
| ~ spl155_2
| ~ spl155_11 ),
inference(trivial_inequality_removal,[],[f2836]) ).
thf(f2836,plain,
( ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),X0)) )
| ( $false = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) ) )
| ~ spl155_2
| ~ spl155_11 ),
inference(superposition,[],[f2815,f2740]) ).
thf(f7338,plain,
( spl155_334
| ~ spl155_2
| ~ spl155_10 ),
inference(avatar_split_clause,[],[f2829,f2810,f2739,f7336]) ).
thf(f7336,plain,
( spl155_334
<=> ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1)) )
| ( $false = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_334])]) ).
thf(f2829,plain,
( ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1)) )
| ( $false = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) ) )
| ~ spl155_2
| ~ spl155_10 ),
inference(trivial_inequality_removal,[],[f2828]) ).
thf(f2828,plain,
( ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1)) )
| ( $false = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) ) )
| ~ spl155_2
| ~ spl155_10 ),
inference(superposition,[],[f2811,f2740]) ).
thf(f7314,plain,
spl155_333,
inference(avatar_split_clause,[],[f2212,f7312]) ).
thf(f7312,plain,
( spl155_333
<=> ! [X0: set_nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB))))),X1) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X1),X0) )
| ( $true != vAPP(set_nat,$o,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB))))),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_333])]) ).
thf(f2212,plain,
! [X0: set_nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB))))),X1) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X1),X0) )
| ( $true != vAPP(set_nat,$o,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB))))),X0) ) ),
inference(definition_unfolding,[],[f1765,f2098,f1650,f2098]) ).
thf(f1650,plain,
ord_less_eq_set_nat = vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),
inference(cnf_transformation,[],[f395]) ).
thf(f395,plain,
ord_less_eq_set_nat = vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),
inference(fool_elimination,[],[f394]) ).
thf(f394,plain,
( ord_less_eq_set_nat
= ( ^ [X0: set_nat,X1: set_nat] : ( vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X1) = X0 ) ) ),
inference(rectify,[],[f259]) ).
thf(f259,axiom,
( ord_less_eq_set_nat
= ( ^ [X16: set_nat,X17: set_nat] : ( vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X16),X17) = X16 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_258_inf_Oorder__iff) ).
thf(f2098,plain,
finite_finite_nat = vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB))))),
inference(definition_unfolding,[],[f1645,f1646]) ).
thf(f1646,plain,
ord_less_eq_nat = vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),
inference(cnf_transformation,[],[f387]) ).
thf(f387,plain,
ord_less_eq_nat = vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),
inference(fool_elimination,[],[f386]) ).
thf(f386,plain,
( ord_less_eq_nat
= ( ^ [X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X1) = X0 ) ) ),
inference(rectify,[],[f284]) ).
thf(f284,axiom,
( ord_less_eq_nat
= ( ^ [X23: nat,X24: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X23),X24) = X23 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_283_le__iff__inf) ).
thf(f1645,plain,
finite_finite_nat = vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,ord_less_eq_nat)))),
inference(cnf_transformation,[],[f385]) ).
thf(f385,plain,
finite_finite_nat = vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,ord_less_eq_nat)))),
inference(fool_elimination,[],[f384]) ).
thf(f384,plain,
( finite_finite_nat
= ( ^ [X0: set_nat] :
? [X1: nat] :
! [X2: nat] :
( vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X2),X0)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X1) ) ) ),
inference(rectify,[],[f347]) ).
thf(f347,axiom,
( finite_finite_nat
= ( ^ [X63: set_nat] :
? [X64: nat] :
! [X23: nat] :
( vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X23),X63)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X23),X64) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_346_finite__nat__set__iff__bounded__le) ).
thf(f1765,plain,
! [X0: set_nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,finite_finite_nat,X1) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X1),X0) )
| ( $true != vAPP(set_nat,$o,finite_finite_nat,X0) ) ),
inference(cnf_transformation,[],[f1119]) ).
thf(f1119,plain,
! [X0: set_nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,finite_finite_nat,X1) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X1),X0) )
| ( $true != vAPP(set_nat,$o,finite_finite_nat,X0) ) ),
inference(flattening,[],[f1118]) ).
thf(f1118,plain,
! [X0: set_nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,finite_finite_nat,X1) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X1),X0) )
| ( $true != vAPP(set_nat,$o,finite_finite_nat,X0) ) ),
inference(ennf_transformation,[],[f565]) ).
thf(f565,plain,
! [X0: set_nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,finite_finite_nat,X0) )
=> ( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X1),X0) )
=> ( $true = vAPP(set_nat,$o,finite_finite_nat,X1) ) ) ),
inference(fool_elimination,[],[f564]) ).
thf(f564,plain,
! [X0: set_nat,X1: set_nat] :
( vAPP(set_nat,$o,finite_finite_nat,X0)
=> ( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X1),X0)
=> vAPP(set_nat,$o,finite_finite_nat,X1) ) ),
inference(rectify,[],[f322]) ).
thf(f322,axiom,
! [X3: set_nat,X2: set_nat] :
( vAPP(set_nat,$o,finite_finite_nat,X3)
=> ( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X3)
=> vAPP(set_nat,$o,finite_finite_nat,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_321_rev__finite__subset) ).
thf(f7310,plain,
( spl155_332
| ~ spl155_245
| ~ spl155_246 ),
inference(avatar_split_clause,[],[f6140,f6132,f6127,f7307]) ).
thf(f7307,plain,
( spl155_332
<=> ( vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,c) = vAPP(list_nat,set_nat,set_nat2,vAPP(set_nat,list_nat,sK8,vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,c))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_332])]) ).
thf(f6140,plain,
( ( vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,c) = vAPP(list_nat,set_nat,set_nat2,vAPP(set_nat,list_nat,sK8,vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,c))) )
| ~ spl155_245
| ~ spl155_246 ),
inference(trivial_inequality_removal,[],[f6135]) ).
thf(f6135,plain,
( ( $true != $true )
| ( vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,c) = vAPP(list_nat,set_nat,set_nat2,vAPP(set_nat,list_nat,sK8,vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,c))) )
| ~ spl155_245
| ~ spl155_246 ),
inference(superposition,[],[f6133,f6129]) ).
thf(f7301,plain,
spl155_331,
inference(avatar_split_clause,[],[f2224,f7299]) ).
thf(f7299,plain,
( spl155_331
<=> ! [X0: product_prod_nat_nat > a,X1: nat] :
( ( $true = vAPP(set_nat,$o,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB))))),vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),adjacent_nodes_a,X0),X1)) )
| ( $true != vAPP(sTfun(product_prod_nat_nat,a),$o,vAPP(sTfun(sTfun(product_prod_nat_nat,a),set_nat),sTfun(sTfun(product_prod_nat_nat,a),$o),vAPP(sTfun(set_nat,$o),sTfun(sTfun(sTfun(product_prod_nat_nat,a),set_nat),sTfun(sTfun(product_prod_nat_nat,a),$o)),bCOMB,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB)))))),v_a),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_331])]) ).
thf(f2224,plain,
! [X0: product_prod_nat_nat > a,X1: nat] :
( ( $true = vAPP(set_nat,$o,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB))))),vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),adjacent_nodes_a,X0),X1)) )
| ( $true != vAPP(sTfun(product_prod_nat_nat,a),$o,vAPP(sTfun(sTfun(product_prod_nat_nat,a),set_nat),sTfun(sTfun(product_prod_nat_nat,a),$o),vAPP(sTfun(set_nat,$o),sTfun(sTfun(sTfun(product_prod_nat_nat,a),set_nat),sTfun(sTfun(product_prod_nat_nat,a),$o)),bCOMB,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB)))))),v_a),X0) ) ),
inference(definition_unfolding,[],[f1777,f2098,f2099]) ).
thf(f2099,plain,
finite_Graph_a = vAPP(sTfun(sTfun(product_prod_nat_nat,a),set_nat),sTfun(sTfun(product_prod_nat_nat,a),$o),vAPP(sTfun(set_nat,$o),sTfun(sTfun(sTfun(product_prod_nat_nat,a),set_nat),sTfun(sTfun(product_prod_nat_nat,a),$o)),bCOMB,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB)))))),v_a),
inference(definition_unfolding,[],[f1644,f2098]) ).
thf(f1644,plain,
finite_Graph_a = vAPP(sTfun(sTfun(product_prod_nat_nat,a),set_nat),sTfun(sTfun(product_prod_nat_nat,a),$o),vAPP(sTfun(set_nat,$o),sTfun(sTfun(sTfun(product_prod_nat_nat,a),set_nat),sTfun(sTfun(product_prod_nat_nat,a),$o)),bCOMB,finite_finite_nat),v_a),
inference(cnf_transformation,[],[f383]) ).
thf(f383,plain,
finite_Graph_a = vAPP(sTfun(sTfun(product_prod_nat_nat,a),set_nat),sTfun(sTfun(product_prod_nat_nat,a),$o),vAPP(sTfun(set_nat,$o),sTfun(sTfun(sTfun(product_prod_nat_nat,a),set_nat),sTfun(sTfun(product_prod_nat_nat,a),$o)),bCOMB,finite_finite_nat),v_a),
inference(fool_elimination,[],[f382]) ).
thf(f382,plain,
( finite_Graph_a
= ( ^ [X0: product_prod_nat_nat > a] : vAPP(set_nat,$o,finite_finite_nat,vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0)) ) ),
inference(rectify,[],[f224]) ).
thf(f224,axiom,
( finite_Graph_a
= ( ^ [X41: product_prod_nat_nat > a] : vAPP(set_nat,$o,finite_finite_nat,vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X41)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_Finite__Graph__def) ).
thf(f1777,plain,
! [X0: product_prod_nat_nat > a,X1: nat] :
( ( $true = vAPP(set_nat,$o,finite_finite_nat,vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),adjacent_nodes_a,X0),X1)) )
| ( $true != vAPP(sTfun(product_prod_nat_nat,a),$o,finite_Graph_a,X0) ) ),
inference(cnf_transformation,[],[f1134]) ).
thf(f1134,plain,
! [X0: product_prod_nat_nat > a,X1: nat] :
( ( $true = vAPP(set_nat,$o,finite_finite_nat,vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),adjacent_nodes_a,X0),X1)) )
| ( $true != vAPP(sTfun(product_prod_nat_nat,a),$o,finite_Graph_a,X0) ) ),
inference(ennf_transformation,[],[f581]) ).
thf(f581,plain,
! [X0: product_prod_nat_nat > a,X1: nat] :
( ( $true = vAPP(sTfun(product_prod_nat_nat,a),$o,finite_Graph_a,X0) )
=> ( $true = vAPP(set_nat,$o,finite_finite_nat,vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),adjacent_nodes_a,X0),X1)) ) ),
inference(fool_elimination,[],[f580]) ).
thf(f580,plain,
! [X0: product_prod_nat_nat > a,X1: nat] :
( vAPP(sTfun(product_prod_nat_nat,a),$o,finite_Graph_a,X0)
=> vAPP(set_nat,$o,finite_finite_nat,vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),adjacent_nodes_a,X0),X1)) ),
inference(rectify,[],[f227]) ).
thf(f227,axiom,
! [X9: product_prod_nat_nat > a,X1: nat] :
( vAPP(sTfun(product_prod_nat_nat,a),$o,finite_Graph_a,X9)
=> vAPP(set_nat,$o,finite_finite_nat,vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),adjacent_nodes_a,X9),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_Finite__Graph_Oadjacent__nodes__finite) ).
thf(f7283,plain,
spl155_330,
inference(avatar_split_clause,[],[f2140,f7281]) ).
thf(f7281,plain,
( spl155_330
<=> ! [X0: product_prod_nat_nat > a] :
( ( $true = vAPP(sTfun(product_prod_nat_nat,a),$o,vAPP(sTfun(sTfun(product_prod_nat_nat,a),set_nat),sTfun(sTfun(product_prod_nat_nat,a),$o),vAPP(sTfun(set_nat,$o),sTfun(sTfun(sTfun(product_prod_nat_nat,a),set_nat),sTfun(sTfun(product_prod_nat_nat,a),$o)),bCOMB,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB)))))),v_a),X0) )
| ( $true != vAPP(set_nat,$o,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB))))),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_330])]) ).
thf(f2140,plain,
! [X0: product_prod_nat_nat > a] :
( ( $true = vAPP(sTfun(product_prod_nat_nat,a),$o,vAPP(sTfun(sTfun(product_prod_nat_nat,a),set_nat),sTfun(sTfun(product_prod_nat_nat,a),$o),vAPP(sTfun(set_nat,$o),sTfun(sTfun(sTfun(product_prod_nat_nat,a),set_nat),sTfun(sTfun(product_prod_nat_nat,a),$o)),bCOMB,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB)))))),v_a),X0) )
| ( $true != vAPP(set_nat,$o,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB))))),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0)) ) ),
inference(definition_unfolding,[],[f1679,f2099,f2098]) ).
thf(f1679,plain,
! [X0: product_prod_nat_nat > a] :
( ( $true = vAPP(sTfun(product_prod_nat_nat,a),$o,finite_Graph_a,X0) )
| ( $true != vAPP(set_nat,$o,finite_finite_nat,vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0)) ) ),
inference(cnf_transformation,[],[f1076]) ).
thf(f1076,plain,
! [X0: product_prod_nat_nat > a] :
( ( $true = vAPP(sTfun(product_prod_nat_nat,a),$o,finite_Graph_a,X0) )
| ( $true != vAPP(set_nat,$o,finite_finite_nat,vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0)) ) ),
inference(ennf_transformation,[],[f453]) ).
thf(f453,plain,
! [X0: product_prod_nat_nat > a] :
( ( $true = vAPP(set_nat,$o,finite_finite_nat,vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0)) )
=> ( $true = vAPP(sTfun(product_prod_nat_nat,a),$o,finite_Graph_a,X0) ) ),
inference(fool_elimination,[],[f452]) ).
thf(f452,plain,
! [X0: product_prod_nat_nat > a] :
( vAPP(set_nat,$o,finite_finite_nat,vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0))
=> vAPP(sTfun(product_prod_nat_nat,a),$o,finite_Graph_a,X0) ),
inference(rectify,[],[f225]) ).
thf(f225,axiom,
! [X9: product_prod_nat_nat > a] :
( vAPP(set_nat,$o,finite_finite_nat,vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X9))
=> vAPP(sTfun(product_prod_nat_nat,a),$o,finite_Graph_a,X9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_Finite__Graph_Ointro) ).
thf(f7279,plain,
spl155_329,
inference(avatar_split_clause,[],[f2134,f7277]) ).
thf(f7277,plain,
( spl155_329
<=> ! [X0: product_prod_nat_nat > a] :
( ( $true = vAPP(set_nat,$o,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB))))),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0)) )
| ( $true != vAPP(sTfun(product_prod_nat_nat,a),$o,vAPP(sTfun(sTfun(product_prod_nat_nat,a),set_nat),sTfun(sTfun(product_prod_nat_nat,a),$o),vAPP(sTfun(set_nat,$o),sTfun(sTfun(sTfun(product_prod_nat_nat,a),set_nat),sTfun(sTfun(product_prod_nat_nat,a),$o)),bCOMB,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB)))))),v_a),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_329])]) ).
thf(f2134,plain,
! [X0: product_prod_nat_nat > a] :
( ( $true = vAPP(set_nat,$o,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB))))),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0)) )
| ( $true != vAPP(sTfun(product_prod_nat_nat,a),$o,vAPP(sTfun(sTfun(product_prod_nat_nat,a),set_nat),sTfun(sTfun(product_prod_nat_nat,a),$o),vAPP(sTfun(set_nat,$o),sTfun(sTfun(sTfun(product_prod_nat_nat,a),set_nat),sTfun(sTfun(product_prod_nat_nat,a),$o)),bCOMB,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB)))))),v_a),X0) ) ),
inference(definition_unfolding,[],[f1673,f2098,f2099]) ).
thf(f1673,plain,
! [X0: product_prod_nat_nat > a] :
( ( $true = vAPP(set_nat,$o,finite_finite_nat,vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0)) )
| ( $true != vAPP(sTfun(product_prod_nat_nat,a),$o,finite_Graph_a,X0) ) ),
inference(cnf_transformation,[],[f1070]) ).
thf(f1070,plain,
! [X0: product_prod_nat_nat > a] :
( ( $true = vAPP(set_nat,$o,finite_finite_nat,vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0)) )
| ( $true != vAPP(sTfun(product_prod_nat_nat,a),$o,finite_Graph_a,X0) ) ),
inference(ennf_transformation,[],[f441]) ).
thf(f441,plain,
! [X0: product_prod_nat_nat > a] :
( ( $true = vAPP(sTfun(product_prod_nat_nat,a),$o,finite_Graph_a,X0) )
=> ( $true = vAPP(set_nat,$o,finite_finite_nat,vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0)) ) ),
inference(fool_elimination,[],[f440]) ).
thf(f440,plain,
! [X0: product_prod_nat_nat > a] :
( vAPP(sTfun(product_prod_nat_nat,a),$o,finite_Graph_a,X0)
=> vAPP(set_nat,$o,finite_finite_nat,vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0)) ),
inference(rectify,[],[f226]) ).
thf(f226,axiom,
! [X9: product_prod_nat_nat > a] :
( vAPP(sTfun(product_prod_nat_nat,a),$o,finite_Graph_a,X9)
=> vAPP(set_nat,$o,finite_finite_nat,vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X9)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_Finite__Graph_Ofinite__V) ).
thf(f7223,plain,
spl155_328,
inference(avatar_split_clause,[],[f2183,f7221]) ).
thf(f7221,plain,
( spl155_328
<=> ! [X0: set_nat,X1: nat] :
( ( $true = vAPP(set_nat,$o,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB))))),vAPP(set_nat,set_nat,vAPP(nat,sTfun(set_nat,set_nat),sK10,X1),X0)) )
| ( $true = vAPP(set_nat,$o,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB))))),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_328])]) ).
thf(f2183,plain,
! [X0: set_nat,X1: nat] :
( ( $true = vAPP(set_nat,$o,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB))))),vAPP(set_nat,set_nat,vAPP(nat,sTfun(set_nat,set_nat),sK10,X1),X0)) )
| ( $true = vAPP(set_nat,$o,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB))))),X0) ) ),
inference(definition_unfolding,[],[f1726,f2098,f2098]) ).
thf(f1726,plain,
! [X0: set_nat,X1: nat] :
( ( $true = vAPP(set_nat,$o,finite_finite_nat,vAPP(set_nat,set_nat,vAPP(nat,sTfun(set_nat,set_nat),sK10,X1),X0)) )
| ( $true = vAPP(set_nat,$o,finite_finite_nat,X0) ) ),
inference(cnf_transformation,[],[f1446]) ).
thf(f1446,plain,
! [X0: set_nat,X1: nat] :
( ( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,vAPP(nat,sTfun(set_nat,set_nat),sK10,X1),X0)),X0) )
& ( vAPP(set_nat,nat,finite_card_nat,vAPP(set_nat,set_nat,vAPP(nat,sTfun(set_nat,set_nat),sK10,X1),X0)) = X1 )
& ( $true = vAPP(set_nat,$o,finite_finite_nat,vAPP(set_nat,set_nat,vAPP(nat,sTfun(set_nat,set_nat),sK10,X1),X0)) ) )
| ( $true = vAPP(set_nat,$o,finite_finite_nat,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f1095,f1445]) ).
thf(f1445,plain,
! [X0: set_nat,X1: nat] :
( ? [X2: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X0) )
& ( vAPP(set_nat,nat,finite_card_nat,X2) = X1 )
& ( vAPP(set_nat,$o,finite_finite_nat,X2) = $true ) )
=> ( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,vAPP(nat,sTfun(set_nat,set_nat),sK10,X1),X0)),X0) )
& ( vAPP(set_nat,nat,finite_card_nat,vAPP(set_nat,set_nat,vAPP(nat,sTfun(set_nat,set_nat),sK10,X1),X0)) = X1 )
& ( $true = vAPP(set_nat,$o,finite_finite_nat,vAPP(set_nat,set_nat,vAPP(nat,sTfun(set_nat,set_nat),sK10,X1),X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1095,plain,
! [X0: set_nat,X1: nat] :
( ? [X2: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X0) )
& ( vAPP(set_nat,nat,finite_card_nat,X2) = X1 )
& ( vAPP(set_nat,$o,finite_finite_nat,X2) = $true ) )
| ( $true = vAPP(set_nat,$o,finite_finite_nat,X0) ) ),
inference(ennf_transformation,[],[f1041]) ).
thf(f1041,plain,
! [X0: set_nat,X1: nat] :
( ( $true != vAPP(set_nat,$o,finite_finite_nat,X0) )
=> ? [X2: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X0) )
& ( vAPP(set_nat,nat,finite_card_nat,X2) = X1 )
& ( vAPP(set_nat,$o,finite_finite_nat,X2) = $true ) ) ),
inference(flattening,[],[f535]) ).
thf(f535,plain,
! [X0: set_nat,X1: nat] :
( ( $true != vAPP(set_nat,$o,finite_finite_nat,X0) )
=> ? [X2: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X0) )
& ( vAPP(set_nat,nat,finite_card_nat,X2) = X1 )
& ( vAPP(set_nat,$o,finite_finite_nat,X2) = $true ) ) ),
inference(fool_elimination,[],[f534]) ).
thf(f534,plain,
! [X0: set_nat,X1: nat] :
( ~ vAPP(set_nat,$o,finite_finite_nat,X0)
=> ? [X2: set_nat] :
( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X0)
& ( vAPP(set_nat,nat,finite_card_nat,X2) = X1 )
& vAPP(set_nat,$o,finite_finite_nat,X2) ) ),
inference(rectify,[],[f332]) ).
thf(f332,axiom,
! [X2: set_nat,X48: nat] :
( ~ vAPP(set_nat,$o,finite_finite_nat,X2)
=> ? [X49: set_nat] :
( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X49),X2)
& ( vAPP(set_nat,nat,finite_card_nat,X49) = X48 )
& vAPP(set_nat,$o,finite_finite_nat,X49) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_331_infinite__arbitrarily__large) ).
thf(f7212,plain,
spl155_327,
inference(avatar_split_clause,[],[f2180,f7210]) ).
thf(f7210,plain,
( spl155_327
<=> ! [X0: set_nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB))))),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X1)) )
| ( $true != vAPP(set_nat,$o,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB))))),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_327])]) ).
thf(f2180,plain,
! [X0: set_nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB))))),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X1)) )
| ( $true != vAPP(set_nat,$o,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB))))),X0) ) ),
inference(definition_unfolding,[],[f1722,f2098,f2098]) ).
thf(f1722,plain,
! [X0: set_nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,finite_finite_nat,vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X1)) )
| ( $true != vAPP(set_nat,$o,finite_finite_nat,X0) ) ),
inference(cnf_transformation,[],[f1093]) ).
thf(f1093,plain,
! [X0: set_nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,finite_finite_nat,vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X1)) )
| ( ( $true != vAPP(set_nat,$o,finite_finite_nat,X1) )
& ( $true != vAPP(set_nat,$o,finite_finite_nat,X0) ) ) ),
inference(ennf_transformation,[],[f531]) ).
thf(f531,plain,
! [X0: set_nat,X1: set_nat] :
( ( ( $true = vAPP(set_nat,$o,finite_finite_nat,X1) )
| ( $true = vAPP(set_nat,$o,finite_finite_nat,X0) ) )
=> ( $true = vAPP(set_nat,$o,finite_finite_nat,vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X1)) ) ),
inference(fool_elimination,[],[f530]) ).
thf(f530,plain,
! [X0: set_nat,X1: set_nat] :
( ( vAPP(set_nat,$o,finite_finite_nat,X1)
| vAPP(set_nat,$o,finite_finite_nat,X0) )
=> vAPP(set_nat,$o,finite_finite_nat,vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X1)) ),
inference(rectify,[],[f203]) ).
thf(f203,axiom,
! [X38: set_nat,X39: set_nat] :
( ( vAPP(set_nat,$o,finite_finite_nat,X39)
| vAPP(set_nat,$o,finite_finite_nat,X38) )
=> vAPP(set_nat,$o,finite_finite_nat,vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X38),X39)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_finite__Int) ).
thf(f7208,plain,
spl155_326,
inference(avatar_split_clause,[],[f2179,f7206]) ).
thf(f7206,plain,
( spl155_326
<=> ! [X0: set_nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB))))),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X1)) )
| ( $true != vAPP(set_nat,$o,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB))))),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_326])]) ).
thf(f2179,plain,
! [X0: set_nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB))))),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X1)) )
| ( $true != vAPP(set_nat,$o,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB))))),X1) ) ),
inference(definition_unfolding,[],[f1723,f2098,f2098]) ).
thf(f1723,plain,
! [X0: set_nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,finite_finite_nat,vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X1)) )
| ( $true != vAPP(set_nat,$o,finite_finite_nat,X1) ) ),
inference(cnf_transformation,[],[f1093]) ).
thf(f7190,plain,
spl155_325,
inference(avatar_split_clause,[],[f2211,f7188]) ).
thf(f7188,plain,
( spl155_325
<=> ! [X0: set_nat,X1: set_nat] :
( ( X0 = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_nat,nat,finite_card_nat,X0)),vAPP(set_nat,nat,finite_card_nat,X1)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X1),X0) )
| ( $true != vAPP(set_nat,$o,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB))))),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_325])]) ).
thf(f2211,plain,
! [X0: set_nat,X1: set_nat] :
( ( X0 = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_nat,nat,finite_card_nat,X0)),vAPP(set_nat,nat,finite_card_nat,X1)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X1),X0) )
| ( $true != vAPP(set_nat,$o,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB))))),X0) ) ),
inference(definition_unfolding,[],[f1764,f1646,f1650,f2098]) ).
thf(f1764,plain,
! [X0: set_nat,X1: set_nat] :
( ( X0 = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,finite_card_nat,X0)),vAPP(set_nat,nat,finite_card_nat,X1)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X1),X0) )
| ( $true != vAPP(set_nat,$o,finite_finite_nat,X0) ) ),
inference(cnf_transformation,[],[f1117]) ).
thf(f1117,plain,
! [X0: set_nat,X1: set_nat] :
( ( X0 = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,finite_card_nat,X0)),vAPP(set_nat,nat,finite_card_nat,X1)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X1),X0) )
| ( $true != vAPP(set_nat,$o,finite_finite_nat,X0) ) ),
inference(flattening,[],[f1116]) ).
thf(f1116,plain,
! [X0: set_nat,X1: set_nat] :
( ( X0 = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,finite_card_nat,X0)),vAPP(set_nat,nat,finite_card_nat,X1)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X1),X0) )
| ( $true != vAPP(set_nat,$o,finite_finite_nat,X0) ) ),
inference(ennf_transformation,[],[f563]) ).
thf(f563,plain,
! [X0: set_nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,finite_finite_nat,X0) )
=> ( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X1),X0) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,finite_card_nat,X0)),vAPP(set_nat,nat,finite_card_nat,X1)) )
=> ( X0 = X1 ) ) ) ),
inference(fool_elimination,[],[f562]) ).
thf(f562,plain,
! [X0: set_nat,X1: set_nat] :
( vAPP(set_nat,$o,finite_finite_nat,X0)
=> ( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X1),X0)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,finite_card_nat,X0)),vAPP(set_nat,nat,finite_card_nat,X1))
=> ( X0 = X1 ) ) ) ),
inference(rectify,[],[f215]) ).
thf(f215,axiom,
! [X3: set_nat,X2: set_nat] :
( vAPP(set_nat,$o,finite_finite_nat,X3)
=> ( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X3)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,finite_card_nat,X3)),vAPP(set_nat,nat,finite_card_nat,X2))
=> ( X2 = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_card__seteq) ).
thf(f7172,plain,
spl155_324,
inference(avatar_split_clause,[],[f2213,f7170]) ).
thf(f7170,plain,
( spl155_324
<=> ! [X0: set_nat,X1: set_nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_nat,nat,finite_card_nat,X1)),vAPP(set_nat,nat,finite_card_nat,X0)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X1),X0) )
| ( $true != vAPP(set_nat,$o,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB))))),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_324])]) ).
thf(f2213,plain,
! [X0: set_nat,X1: set_nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_nat,nat,finite_card_nat,X1)),vAPP(set_nat,nat,finite_card_nat,X0)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X1),X0) )
| ( $true != vAPP(set_nat,$o,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB))))),X0) ) ),
inference(definition_unfolding,[],[f1766,f1646,f1650,f2098]) ).
thf(f1766,plain,
! [X0: set_nat,X1: set_nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,finite_card_nat,X1)),vAPP(set_nat,nat,finite_card_nat,X0)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X1),X0) )
| ( $true != vAPP(set_nat,$o,finite_finite_nat,X0) ) ),
inference(cnf_transformation,[],[f1121]) ).
thf(f1121,plain,
! [X0: set_nat,X1: set_nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,finite_card_nat,X1)),vAPP(set_nat,nat,finite_card_nat,X0)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X1),X0) )
| ( $true != vAPP(set_nat,$o,finite_finite_nat,X0) ) ),
inference(flattening,[],[f1120]) ).
thf(f1120,plain,
! [X0: set_nat,X1: set_nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,finite_card_nat,X1)),vAPP(set_nat,nat,finite_card_nat,X0)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X1),X0) )
| ( $true != vAPP(set_nat,$o,finite_finite_nat,X0) ) ),
inference(ennf_transformation,[],[f567]) ).
thf(f567,plain,
! [X0: set_nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,finite_finite_nat,X0) )
=> ( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X1),X0) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,finite_card_nat,X1)),vAPP(set_nat,nat,finite_card_nat,X0)) ) ) ),
inference(fool_elimination,[],[f566]) ).
thf(f566,plain,
! [X0: set_nat,X1: set_nat] :
( vAPP(set_nat,$o,finite_finite_nat,X0)
=> ( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X1),X0)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,finite_card_nat,X1)),vAPP(set_nat,nat,finite_card_nat,X0)) ) ),
inference(rectify,[],[f213]) ).
thf(f213,axiom,
! [X3: set_nat,X2: set_nat] :
( vAPP(set_nat,$o,finite_finite_nat,X3)
=> ( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X3)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,finite_card_nat,X2)),vAPP(set_nat,nat,finite_card_nat,X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_card__mono) ).
thf(f7164,plain,
spl155_323,
inference(avatar_split_clause,[],[f2340,f7162]) ).
thf(f7162,plain,
( spl155_323
<=> ! [X2: nat,X0: product_prod_nat_nat > a,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,X0),X1),X2))),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,X0))) )
| ( $true != vAPP(sTfun(product_prod_nat_nat,a),$o,vAPP(sTfun(sTfun(product_prod_nat_nat,a),set_nat),sTfun(sTfun(product_prod_nat_nat,a),$o),vAPP(sTfun(set_nat,$o),sTfun(sTfun(sTfun(product_prod_nat_nat,a),set_nat),sTfun(sTfun(product_prod_nat_nat,a),$o)),bCOMB,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB)))))),v_a),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_323])]) ).
thf(f2340,plain,
! [X2: nat,X0: product_prod_nat_nat > a,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,X0),X1),X2))),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,X0))) )
| ( $true != vAPP(sTfun(product_prod_nat_nat,a),$o,vAPP(sTfun(sTfun(product_prod_nat_nat,a),set_nat),sTfun(sTfun(product_prod_nat_nat,a),$o),vAPP(sTfun(set_nat,$o),sTfun(sTfun(sTfun(product_prod_nat_nat,a),set_nat),sTfun(sTfun(product_prod_nat_nat,a),$o)),bCOMB,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB)))))),v_a),X0) ) ),
inference(definition_unfolding,[],[f1906,f1646,f2100]) ).
thf(f2100,plain,
edmond1517640972ysis_a = vAPP(sTfun(sTfun(product_prod_nat_nat,a),set_nat),sTfun(sTfun(product_prod_nat_nat,a),$o),vAPP(sTfun(set_nat,$o),sTfun(sTfun(sTfun(product_prod_nat_nat,a),set_nat),sTfun(sTfun(product_prod_nat_nat,a),$o)),bCOMB,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB)))))),v_a),
inference(definition_unfolding,[],[f1621,f2099]) ).
thf(f1621,plain,
edmond1517640972ysis_a = finite_Graph_a,
inference(cnf_transformation,[],[f22]) ).
thf(f22,axiom,
edmond1517640972ysis_a = finite_Graph_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_ek__analysis__def) ).
thf(f1906,plain,
! [X2: nat,X0: product_prod_nat_nat > a,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,X0),X1),X2))),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,X0))) )
| ( $true != vAPP(sTfun(product_prod_nat_nat,a),$o,edmond1517640972ysis_a,X0) ) ),
inference(cnf_transformation,[],[f1222]) ).
thf(f1222,plain,
! [X0: product_prod_nat_nat > a,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,X0),X1),X2))),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,X0))) )
| ( $true != vAPP(sTfun(product_prod_nat_nat,a),$o,edmond1517640972ysis_a,X0) ) ),
inference(ennf_transformation,[],[f775]) ).
thf(f775,plain,
! [X0: product_prod_nat_nat > a,X1: nat,X2: nat] :
( ( $true = vAPP(sTfun(product_prod_nat_nat,a),$o,edmond1517640972ysis_a,X0) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,X0),X1),X2))),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,X0))) ) ),
inference(fool_elimination,[],[f774]) ).
thf(f774,plain,
! [X0: product_prod_nat_nat > a,X1: nat,X2: nat] :
( vAPP(sTfun(product_prod_nat_nat,a),$o,edmond1517640972ysis_a,X0)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,X0),X1),X2))),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,X0))) ),
inference(rectify,[],[f195]) ).
thf(f195,axiom,
! [X9: product_prod_nat_nat > a,X10: nat,X11: nat] :
( vAPP(sTfun(product_prod_nat_nat,a),$o,edmond1517640972ysis_a,X9)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,X9),X10),X11))),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,X9))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_ek__analysis_Ocard__spEdges__le) ).
thf(f7156,plain,
spl155_322,
inference(avatar_split_clause,[],[f2339,f7154]) ).
thf(f2339,plain,
! [X2: nat,X0: product_prod_nat_nat > a,X1: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,X0),X1),X2)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) )
| ( $true != vAPP(sTfun(product_prod_nat_nat,a),$o,vAPP(sTfun(sTfun(product_prod_nat_nat,a),set_nat),sTfun(sTfun(product_prod_nat_nat,a),$o),vAPP(sTfun(set_nat,$o),sTfun(sTfun(sTfun(product_prod_nat_nat,a),set_nat),sTfun(sTfun(product_prod_nat_nat,a),$o)),bCOMB,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB)))))),v_a),X0) ) ),
inference(definition_unfolding,[],[f1905,f1656,f2100]) ).
thf(f1656,plain,
ord_le841296385at_nat = vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),
inference(cnf_transformation,[],[f407]) ).
thf(f407,plain,
ord_le841296385at_nat = vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),
inference(fool_elimination,[],[f406]) ).
thf(f406,plain,
( ord_le841296385at_nat
= ( ^ [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] : ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1) = X0 ) ) ),
inference(rectify,[],[f258]) ).
thf(f258,axiom,
( ord_le841296385at_nat
= ( ^ [X16: set_Pr1986765409at_nat,X17: set_Pr1986765409at_nat] : ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X16),X17) = X16 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_257_inf_Oorder__iff) ).
thf(f1905,plain,
! [X2: nat,X0: product_prod_nat_nat > a,X1: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,X0),X1),X2)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) )
| ( $true != vAPP(sTfun(product_prod_nat_nat,a),$o,edmond1517640972ysis_a,X0) ) ),
inference(cnf_transformation,[],[f1221]) ).
thf(f1221,plain,
! [X0: product_prod_nat_nat > a,X1: nat,X2: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,X0),X1),X2)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) )
| ( $true != vAPP(sTfun(product_prod_nat_nat,a),$o,edmond1517640972ysis_a,X0) ) ),
inference(ennf_transformation,[],[f773]) ).
thf(f773,plain,
! [X0: product_prod_nat_nat > a,X1: nat,X2: nat] :
( ( $true = vAPP(sTfun(product_prod_nat_nat,a),$o,edmond1517640972ysis_a,X0) )
=> ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,X0),X1),X2)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) ) ),
inference(fool_elimination,[],[f772]) ).
thf(f772,plain,
! [X0: product_prod_nat_nat > a,X1: nat,X2: nat] :
( vAPP(sTfun(product_prod_nat_nat,a),$o,edmond1517640972ysis_a,X0)
=> vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,X0),X1),X2)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) ),
inference(rectify,[],[f27]) ).
thf(f27,axiom,
! [X9: product_prod_nat_nat > a,X10: nat,X11: nat] :
( vAPP(sTfun(product_prod_nat_nat,a),$o,edmond1517640972ysis_a,X9)
=> vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,X9),X10),X11)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X9)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_ek__analysis_OspEdges__ss__E) ).
thf(f7117,plain,
spl155_321,
inference(avatar_split_clause,[],[f2217,f7115]) ).
thf(f7115,plain,
( spl155_321
<=> ! [X0: set_nat,X1: nat,X3: nat] :
( ( vAPP(set_nat,nat,vAPP(nat,sTfun(set_nat,nat),sK23,X1),X0) = X3 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X3),vAPP(set_nat,nat,vAPP(nat,sTfun(set_nat,nat),sK23,X1),X0)) )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X3),X0) )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X1),X0) )
| ( $true != vAPP(set_nat,$o,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB))))),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_321])]) ).
thf(f2217,plain,
! [X3: nat,X0: set_nat,X1: nat] :
( ( vAPP(set_nat,nat,vAPP(nat,sTfun(set_nat,nat),sK23,X1),X0) = X3 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X3),vAPP(set_nat,nat,vAPP(nat,sTfun(set_nat,nat),sK23,X1),X0)) )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X3),X0) )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X1),X0) )
| ( $true != vAPP(set_nat,$o,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB))))),X0) ) ),
inference(definition_unfolding,[],[f1772,f1646,f2098]) ).
thf(f1772,plain,
! [X3: nat,X0: set_nat,X1: nat] :
( ( vAPP(set_nat,nat,vAPP(nat,sTfun(set_nat,nat),sK23,X1),X0) = X3 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),vAPP(set_nat,nat,vAPP(nat,sTfun(set_nat,nat),sK23,X1),X0)) )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X3),X0) )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X1),X0) )
| ( $true != vAPP(set_nat,$o,finite_finite_nat,X0) ) ),
inference(cnf_transformation,[],[f1476]) ).
thf(f1476,plain,
! [X0: set_nat,X1: nat] :
( ( ! [X3: nat] :
( ( vAPP(set_nat,nat,vAPP(nat,sTfun(set_nat,nat),sK23,X1),X0) = X3 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),vAPP(set_nat,nat,vAPP(nat,sTfun(set_nat,nat),sK23,X1),X0)) )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X3),X0) ) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,vAPP(nat,sTfun(set_nat,nat),sK23,X1),X0)),X1) )
& ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,vAPP(set_nat,nat,vAPP(nat,sTfun(set_nat,nat),sK23,X1),X0)),X0) ) )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X1),X0) )
| ( $true != vAPP(set_nat,$o,finite_finite_nat,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK23])],[f1125,f1475]) ).
thf(f1475,plain,
! [X0: set_nat,X1: nat] :
( ? [X2: nat] :
( ! [X3: nat] :
( ( X2 = X3 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X2) )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X3),X0) ) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X1) )
& ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X2),X0) ) )
=> ( ! [X3: nat] :
( ( vAPP(set_nat,nat,vAPP(nat,sTfun(set_nat,nat),sK23,X1),X0) = X3 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),vAPP(set_nat,nat,vAPP(nat,sTfun(set_nat,nat),sK23,X1),X0)) )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X3),X0) ) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,vAPP(nat,sTfun(set_nat,nat),sK23,X1),X0)),X1) )
& ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,vAPP(set_nat,nat,vAPP(nat,sTfun(set_nat,nat),sK23,X1),X0)),X0) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1125,plain,
! [X0: set_nat,X1: nat] :
( ? [X2: nat] :
( ! [X3: nat] :
( ( X2 = X3 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X2) )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X3),X0) ) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X1) )
& ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X2),X0) ) )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X1),X0) )
| ( $true != vAPP(set_nat,$o,finite_finite_nat,X0) ) ),
inference(flattening,[],[f1124]) ).
thf(f1124,plain,
! [X0: set_nat,X1: nat] :
( ? [X2: nat] :
( ! [X3: nat] :
( ( X2 = X3 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X2) )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X3),X0) ) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X1) )
& ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X2),X0) ) )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X1),X0) )
| ( $true != vAPP(set_nat,$o,finite_finite_nat,X0) ) ),
inference(ennf_transformation,[],[f571]) ).
thf(f571,plain,
! [X0: set_nat,X1: nat] :
( ( $true = vAPP(set_nat,$o,finite_finite_nat,X0) )
=> ( ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X1),X0) )
=> ? [X2: nat] :
( ! [X3: nat] :
( ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X3),X0) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X2) )
=> ( X2 = X3 ) ) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X1) )
& ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X2),X0) ) ) ) ),
inference(fool_elimination,[],[f570]) ).
thf(f570,plain,
! [X0: set_nat,X1: nat] :
( vAPP(set_nat,$o,finite_finite_nat,X0)
=> ( vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X1),X0)
=> ? [X2: nat] :
( ! [X3: nat] :
( vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X3),X0)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X2)
=> ( X2 = X3 ) ) )
& vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X1)
& vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X2),X0) ) ) ),
inference(rectify,[],[f236]) ).
thf(f236,axiom,
! [X2: set_nat,X13: nat] :
( vAPP(set_nat,$o,finite_finite_nat,X2)
=> ( vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X13),X2)
=> ? [X4: nat] :
( ! [X42: nat] :
( vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X42),X2)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X42),X4)
=> ( X4 = X42 ) ) )
& vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X13)
& vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X4),X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_finite__has__minimal2) ).
thf(f7113,plain,
spl155_320,
inference(avatar_split_clause,[],[f2214,f7111]) ).
thf(f7111,plain,
( spl155_320
<=> ! [X0: set_nat,X1: nat,X3: nat] :
( ( vAPP(set_nat,nat,vAPP(nat,sTfun(set_nat,nat),sK22,X1),X0) = X3 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_nat,nat,vAPP(nat,sTfun(set_nat,nat),sK22,X1),X0)),X3) )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X3),X0) )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X1),X0) )
| ( $true != vAPP(set_nat,$o,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB))))),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_320])]) ).
thf(f2214,plain,
! [X3: nat,X0: set_nat,X1: nat] :
( ( vAPP(set_nat,nat,vAPP(nat,sTfun(set_nat,nat),sK22,X1),X0) = X3 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_nat,nat,vAPP(nat,sTfun(set_nat,nat),sK22,X1),X0)),X3) )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X3),X0) )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X1),X0) )
| ( $true != vAPP(set_nat,$o,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB))))),X0) ) ),
inference(definition_unfolding,[],[f1769,f1646,f2098]) ).
thf(f1769,plain,
! [X3: nat,X0: set_nat,X1: nat] :
( ( vAPP(set_nat,nat,vAPP(nat,sTfun(set_nat,nat),sK22,X1),X0) = X3 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,vAPP(nat,sTfun(set_nat,nat),sK22,X1),X0)),X3) )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X3),X0) )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X1),X0) )
| ( $true != vAPP(set_nat,$o,finite_finite_nat,X0) ) ),
inference(cnf_transformation,[],[f1474]) ).
thf(f1474,plain,
! [X0: set_nat,X1: nat] :
( ( ! [X3: nat] :
( ( vAPP(set_nat,nat,vAPP(nat,sTfun(set_nat,nat),sK22,X1),X0) = X3 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,vAPP(nat,sTfun(set_nat,nat),sK22,X1),X0)),X3) )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X3),X0) ) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),vAPP(set_nat,nat,vAPP(nat,sTfun(set_nat,nat),sK22,X1),X0)) )
& ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,vAPP(set_nat,nat,vAPP(nat,sTfun(set_nat,nat),sK22,X1),X0)),X0) ) )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X1),X0) )
| ( $true != vAPP(set_nat,$o,finite_finite_nat,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK22])],[f1123,f1473]) ).
thf(f1473,plain,
! [X0: set_nat,X1: nat] :
( ? [X2: nat] :
( ! [X3: nat] :
( ( X2 = X3 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X3),X0) ) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
& ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X2),X0) ) )
=> ( ! [X3: nat] :
( ( vAPP(set_nat,nat,vAPP(nat,sTfun(set_nat,nat),sK22,X1),X0) = X3 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,vAPP(nat,sTfun(set_nat,nat),sK22,X1),X0)),X3) )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X3),X0) ) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),vAPP(set_nat,nat,vAPP(nat,sTfun(set_nat,nat),sK22,X1),X0)) )
& ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,vAPP(set_nat,nat,vAPP(nat,sTfun(set_nat,nat),sK22,X1),X0)),X0) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1123,plain,
! [X0: set_nat,X1: nat] :
( ? [X2: nat] :
( ! [X3: nat] :
( ( X2 = X3 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X3),X0) ) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
& ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X2),X0) ) )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X1),X0) )
| ( $true != vAPP(set_nat,$o,finite_finite_nat,X0) ) ),
inference(flattening,[],[f1122]) ).
thf(f1122,plain,
! [X0: set_nat,X1: nat] :
( ? [X2: nat] :
( ! [X3: nat] :
( ( X2 = X3 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X3),X0) ) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
& ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X2),X0) ) )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X1),X0) )
| ( $true != vAPP(set_nat,$o,finite_finite_nat,X0) ) ),
inference(ennf_transformation,[],[f569]) ).
thf(f569,plain,
! [X0: set_nat,X1: nat] :
( ( $true = vAPP(set_nat,$o,finite_finite_nat,X0) )
=> ( ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X1),X0) )
=> ? [X2: nat] :
( ! [X3: nat] :
( ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X3),X0) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
=> ( X2 = X3 ) ) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
& ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X2),X0) ) ) ) ),
inference(fool_elimination,[],[f568]) ).
thf(f568,plain,
! [X0: set_nat,X1: nat] :
( vAPP(set_nat,$o,finite_finite_nat,X0)
=> ( vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X1),X0)
=> ? [X2: nat] :
( ! [X3: nat] :
( vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X3),X0)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3)
=> ( X2 = X3 ) ) )
& vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2)
& vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X2),X0) ) ) ),
inference(rectify,[],[f239]) ).
thf(f239,axiom,
! [X2: set_nat,X13: nat] :
( vAPP(set_nat,$o,finite_finite_nat,X2)
=> ( vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X13),X2)
=> ? [X4: nat] :
( ! [X42: nat] :
( vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X42),X2)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X42)
=> ( X4 = X42 ) ) )
& vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X13),X4)
& vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X4),X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_finite__has__maximal2) ).
thf(f7105,plain,
spl155_319,
inference(avatar_split_clause,[],[f2132,f7103]) ).
thf(f7103,plain,
( spl155_319
<=> ! [X0: product_prod_nat_nat > a] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,X0)) )
| ( $true != vAPP(sTfun(product_prod_nat_nat,a),$o,vAPP(sTfun(sTfun(product_prod_nat_nat,a),set_nat),sTfun(sTfun(product_prod_nat_nat,a),$o),vAPP(sTfun(set_nat,$o),sTfun(sTfun(sTfun(product_prod_nat_nat,a),set_nat),sTfun(sTfun(product_prod_nat_nat,a),$o)),bCOMB,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB)))))),v_a),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_319])]) ).
thf(f2132,plain,
! [X0: product_prod_nat_nat > a] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,X0)) )
| ( $true != vAPP(sTfun(product_prod_nat_nat,a),$o,vAPP(sTfun(sTfun(product_prod_nat_nat,a),set_nat),sTfun(sTfun(product_prod_nat_nat,a),$o),vAPP(sTfun(set_nat,$o),sTfun(sTfun(sTfun(product_prod_nat_nat,a),set_nat),sTfun(sTfun(product_prod_nat_nat,a),$o)),bCOMB,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB)))))),v_a),X0) ) ),
inference(definition_unfolding,[],[f1671,f1656,f2100]) ).
thf(f1671,plain,
! [X0: product_prod_nat_nat > a] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,X0)) )
| ( $true != vAPP(sTfun(product_prod_nat_nat,a),$o,edmond1517640972ysis_a,X0) ) ),
inference(cnf_transformation,[],[f1068]) ).
thf(f1068,plain,
! [X0: product_prod_nat_nat > a] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,X0)) )
| ( $true != vAPP(sTfun(product_prod_nat_nat,a),$o,edmond1517640972ysis_a,X0) ) ),
inference(ennf_transformation,[],[f437]) ).
thf(f437,plain,
! [X0: product_prod_nat_nat > a] :
( ( $true = vAPP(sTfun(product_prod_nat_nat,a),$o,edmond1517640972ysis_a,X0) )
=> ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,X0)) ) ),
inference(fool_elimination,[],[f436]) ).
thf(f436,plain,
! [X0: product_prod_nat_nat > a] :
( vAPP(sTfun(product_prod_nat_nat,a),$o,edmond1517640972ysis_a,X0)
=> vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,X0)) ),
inference(rectify,[],[f28]) ).
thf(f28,axiom,
! [X9: product_prod_nat_nat > a] :
( vAPP(sTfun(product_prod_nat_nat,a),$o,edmond1517640972ysis_a,X9)
=> vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X9)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,X9)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_ek__analysis_OE__ss__uE) ).
thf(f7073,plain,
spl155_318,
inference(avatar_split_clause,[],[f2218,f7071]) ).
thf(f7071,plain,
( spl155_318
<=> ! [X0: set_nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_nat,nat,vAPP(nat,sTfun(set_nat,nat),sK23,X1),X0)),X1) )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X1),X0) )
| ( $true != vAPP(set_nat,$o,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB))))),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_318])]) ).
thf(f2218,plain,
! [X0: set_nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_nat,nat,vAPP(nat,sTfun(set_nat,nat),sK23,X1),X0)),X1) )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X1),X0) )
| ( $true != vAPP(set_nat,$o,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB))))),X0) ) ),
inference(definition_unfolding,[],[f1771,f1646,f2098]) ).
thf(f1771,plain,
! [X0: set_nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,vAPP(nat,sTfun(set_nat,nat),sK23,X1),X0)),X1) )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X1),X0) )
| ( $true != vAPP(set_nat,$o,finite_finite_nat,X0) ) ),
inference(cnf_transformation,[],[f1476]) ).
thf(f7069,plain,
spl155_317,
inference(avatar_split_clause,[],[f2215,f7067]) ).
thf(f7067,plain,
( spl155_317
<=> ! [X0: set_nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X1),vAPP(set_nat,nat,vAPP(nat,sTfun(set_nat,nat),sK22,X1),X0)) )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X1),X0) )
| ( $true != vAPP(set_nat,$o,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB))))),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_317])]) ).
thf(f2215,plain,
! [X0: set_nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X1),vAPP(set_nat,nat,vAPP(nat,sTfun(set_nat,nat),sK22,X1),X0)) )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X1),X0) )
| ( $true != vAPP(set_nat,$o,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB))))),X0) ) ),
inference(definition_unfolding,[],[f1768,f1646,f2098]) ).
thf(f1768,plain,
! [X0: set_nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),vAPP(set_nat,nat,vAPP(nat,sTfun(set_nat,nat),sK22,X1),X0)) )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X1),X0) )
| ( $true != vAPP(set_nat,$o,finite_finite_nat,X0) ) ),
inference(cnf_transformation,[],[f1474]) ).
thf(f7025,plain,
spl155_316,
inference(avatar_split_clause,[],[f2266,f7023]) ).
thf(f7023,plain,
( spl155_316
<=> ! [X0: nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB))))),vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK27,X1),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),vAPP(set_nat,nat,finite_card_nat,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_316])]) ).
thf(f2266,plain,
! [X0: nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB))))),vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK27,X1),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),vAPP(set_nat,nat,finite_card_nat,X1)) ) ),
inference(definition_unfolding,[],[f1823,f2098,f1646]) ).
thf(f1823,plain,
! [X0: nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,finite_finite_nat,vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK27,X1),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(set_nat,nat,finite_card_nat,X1)) ) ),
inference(cnf_transformation,[],[f1482]) ).
thf(f1482,plain,
! [X0: nat,X1: set_nat] :
( ( ( $true = vAPP(set_nat,$o,finite_finite_nat,vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK27,X1),X0)) )
& ( vAPP(set_nat,nat,finite_card_nat,vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK27,X1),X0)) = X0 )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK27,X1),X0)),X1) ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(set_nat,nat,finite_card_nat,X1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK27])],[f1194,f1481]) ).
thf(f1481,plain,
! [X0: nat,X1: set_nat] :
( ? [X2: set_nat] :
( ( vAPP(set_nat,$o,finite_finite_nat,X2) = $true )
& ( vAPP(set_nat,nat,finite_card_nat,X2) = X0 )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X1) ) )
=> ( ( $true = vAPP(set_nat,$o,finite_finite_nat,vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK27,X1),X0)) )
& ( vAPP(set_nat,nat,finite_card_nat,vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK27,X1),X0)) = X0 )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK27,X1),X0)),X1) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1194,plain,
! [X0: nat,X1: set_nat] :
( ? [X2: set_nat] :
( ( vAPP(set_nat,$o,finite_finite_nat,X2) = $true )
& ( vAPP(set_nat,nat,finite_card_nat,X2) = X0 )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X1) ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(set_nat,nat,finite_card_nat,X1)) ) ),
inference(flattening,[],[f1193]) ).
thf(f1193,plain,
! [X0: nat,X1: set_nat] :
( ? [X2: set_nat] :
( ( vAPP(set_nat,$o,finite_finite_nat,X2) = $true )
& ( vAPP(set_nat,nat,finite_card_nat,X2) = X0 )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X1) ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(set_nat,nat,finite_card_nat,X1)) ) ),
inference(ennf_transformation,[],[f1047]) ).
thf(f1047,plain,
! [X0: nat,X1: set_nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(set_nat,nat,finite_card_nat,X1)) )
=> ~ ! [X2: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X1) )
=> ( ( vAPP(set_nat,nat,finite_card_nat,X2) = X0 )
=> ( vAPP(set_nat,$o,finite_finite_nat,X2) != $true ) ) ) ),
inference(flattening,[],[f667]) ).
thf(f667,plain,
! [X0: nat,X1: set_nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(set_nat,nat,finite_card_nat,X1)) )
=> ~ ! [X2: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X1) )
=> ( ( vAPP(set_nat,nat,finite_card_nat,X2) = X0 )
=> ( vAPP(set_nat,$o,finite_finite_nat,X2) != $true ) ) ) ),
inference(fool_elimination,[],[f666]) ).
thf(f666,plain,
! [X0: nat,X1: set_nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(set_nat,nat,finite_card_nat,X1))
=> ~ ! [X2: set_nat] :
( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X1)
=> ( ( vAPP(set_nat,nat,finite_card_nat,X2) = X0 )
=> ~ vAPP(set_nat,$o,finite_finite_nat,X2) ) ) ),
inference(rectify,[],[f339]) ).
thf(f339,axiom,
! [X48: nat,X45: set_nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X48),vAPP(set_nat,nat,finite_card_nat,X45))
=> ~ ! [X51: set_nat] :
( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X51),X45)
=> ( ( vAPP(set_nat,nat,finite_card_nat,X51) = X48 )
=> ~ vAPP(set_nat,$o,finite_finite_nat,X51) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_338_obtain__subset__with__card__n) ).
thf(f7021,plain,
spl155_315,
inference(avatar_split_clause,[],[f2210,f7019]) ).
thf(f2210,plain,
! [X0: set_nat,X1: set_nat] :
( ( X0 = X1 )
| ( vAPP(set_nat,nat,finite_card_nat,X0) != vAPP(set_nat,nat,finite_card_nat,X1) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X1),X0) )
| ( $true != vAPP(set_nat,$o,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB))))),X0) ) ),
inference(definition_unfolding,[],[f1763,f1650,f2098]) ).
thf(f1763,plain,
! [X0: set_nat,X1: set_nat] :
( ( X0 = X1 )
| ( vAPP(set_nat,nat,finite_card_nat,X0) != vAPP(set_nat,nat,finite_card_nat,X1) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X1),X0) )
| ( $true != vAPP(set_nat,$o,finite_finite_nat,X0) ) ),
inference(cnf_transformation,[],[f1115]) ).
thf(f1115,plain,
! [X0: set_nat,X1: set_nat] :
( ( X0 = X1 )
| ( vAPP(set_nat,nat,finite_card_nat,X0) != vAPP(set_nat,nat,finite_card_nat,X1) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X1),X0) )
| ( $true != vAPP(set_nat,$o,finite_finite_nat,X0) ) ),
inference(flattening,[],[f1114]) ).
thf(f1114,plain,
! [X0: set_nat,X1: set_nat] :
( ( X0 = X1 )
| ( vAPP(set_nat,nat,finite_card_nat,X0) != vAPP(set_nat,nat,finite_card_nat,X1) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X1),X0) )
| ( $true != vAPP(set_nat,$o,finite_finite_nat,X0) ) ),
inference(ennf_transformation,[],[f561]) ).
thf(f561,plain,
! [X0: set_nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,finite_finite_nat,X0) )
=> ( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X1),X0) )
=> ( ( vAPP(set_nat,nat,finite_card_nat,X0) = vAPP(set_nat,nat,finite_card_nat,X1) )
=> ( X0 = X1 ) ) ) ),
inference(fool_elimination,[],[f560]) ).
thf(f560,plain,
! [X0: set_nat,X1: set_nat] :
( vAPP(set_nat,$o,finite_finite_nat,X0)
=> ( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X1),X0)
=> ( ( vAPP(set_nat,nat,finite_card_nat,X0) = vAPP(set_nat,nat,finite_card_nat,X1) )
=> ( X0 = X1 ) ) ) ),
inference(rectify,[],[f334]) ).
thf(f334,axiom,
! [X3: set_nat,X2: set_nat] :
( vAPP(set_nat,$o,finite_finite_nat,X3)
=> ( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X3)
=> ( ( vAPP(set_nat,nat,finite_card_nat,X2) = vAPP(set_nat,nat,finite_card_nat,X3) )
=> ( X2 = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_333_card__subset__eq) ).
thf(f6951,plain,
spl155_314,
inference(avatar_split_clause,[],[f2181,f6949]) ).
thf(f2181,plain,
! [X0: set_nat,X1: nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_nat,set_nat,vAPP(nat,sTfun(set_nat,set_nat),sK10,X1),X0)),X0) )
| ( $true = vAPP(set_nat,$o,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB))))),X0) ) ),
inference(definition_unfolding,[],[f1728,f1650,f2098]) ).
thf(f1728,plain,
! [X0: set_nat,X1: nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,vAPP(nat,sTfun(set_nat,set_nat),sK10,X1),X0)),X0) )
| ( $true = vAPP(set_nat,$o,finite_finite_nat,X0) ) ),
inference(cnf_transformation,[],[f1446]) ).
thf(f6841,plain,
spl155_313,
inference(avatar_split_clause,[],[f2477,f6839]) ).
thf(f6839,plain,
( spl155_313
<=> ! [X0: set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat > set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X1,X3)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X1,vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),set_Pr1986765409at_nat,sK149,X1))),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X1,vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),set_Pr1986765409at_nat,sK150,X1))) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X2),X3) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X1,X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_313])]) ).
thf(f2477,plain,
! [X2: set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat > set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X1,X3)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X1,vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),set_Pr1986765409at_nat,sK149,X1))),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X1,vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),set_Pr1986765409at_nat,sK150,X1))) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X2),X3) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X1,X2)) ) ),
inference(definition_unfolding,[],[f2074,f1656,f1656,f1656,f1656]) ).
thf(f2074,plain,
! [X2: set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat > set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X1,X3)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X1,vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),set_Pr1986765409at_nat,sK149,X1))),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X1,vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),set_Pr1986765409at_nat,sK150,X1))) )
| ( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X2),X3) != $true )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X1,X2)) ) ),
inference(cnf_transformation,[],[f1610]) ).
thf(f1610,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat > set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X1,X3)) )
| ( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X1,vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),set_Pr1986765409at_nat,sK149,X1))),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X1,vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),set_Pr1986765409at_nat,sK150,X1))) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),set_Pr1986765409at_nat,sK149,X1)),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),set_Pr1986765409at_nat,sK150,X1)) ) )
| ( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X2),X3) != $true )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X1,X2)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK149,sK150])],[f1408,f1609]) ).
thf(f1609,plain,
! [X1: set_Pr1986765409at_nat > set_Pr1986765409at_nat] :
( ? [X4: set_Pr1986765409at_nat,X5: set_Pr1986765409at_nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X1,X4)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X1,X5)) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X4),X5) ) )
=> ( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X1,vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),set_Pr1986765409at_nat,sK149,X1))),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X1,vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),set_Pr1986765409at_nat,sK150,X1))) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),set_Pr1986765409at_nat,sK149,X1)),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),set_Pr1986765409at_nat,sK150,X1)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1408,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat > set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X1,X3)) )
| ? [X4: set_Pr1986765409at_nat,X5: set_Pr1986765409at_nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X1,X4)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X1,X5)) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X4),X5) ) )
| ( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X2),X3) != $true )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X1,X2)) ) ),
inference(flattening,[],[f1407]) ).
thf(f1407,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat > set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X1,X3)) )
| ? [X4: set_Pr1986765409at_nat,X5: set_Pr1986765409at_nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X1,X4)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X1,X5)) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X4),X5) ) )
| ( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X2),X3) != $true )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X1,X2)) ) ),
inference(ennf_transformation,[],[f989]) ).
thf(f989,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat > set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X1,X2)) )
=> ( ( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X2),X3) = $true )
=> ( ! [X4: set_Pr1986765409at_nat,X5: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X4),X5) )
=> ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X1,X4)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X1,X5)) ) )
=> ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X1,X3)) ) ) ) ),
inference(fool_elimination,[],[f988]) ).
thf(f988,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat > set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X1,X2))
=> ( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X2),X3)
=> ( ! [X4: set_Pr1986765409at_nat,X5: set_Pr1986765409at_nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X4),X5)
=> vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X1,X4)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X1,X5)) )
=> vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X1,X3)) ) ) ),
inference(rectify,[],[f106]) ).
thf(f106,axiom,
! [X13: set_Pr1986765409at_nat,X25: set_Pr1986765409at_nat > set_Pr1986765409at_nat,X12: set_Pr1986765409at_nat,X9: set_Pr1986765409at_nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X13),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X25,X12))
=> ( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X12),X9)
=> ( ! [X4: set_Pr1986765409at_nat,X26: set_Pr1986765409at_nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X4),X26)
=> vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X25,X4)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X25,X26)) )
=> vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X13),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X25,X9)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_order__subst1) ).
thf(f6837,plain,
spl155_312,
inference(avatar_split_clause,[],[f2475,f6835]) ).
thf(f6835,plain,
( spl155_312
<=> ! [X0: set_Pr1986765409at_nat,X3: nat,X2: nat,X1: nat > set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),vAPP(nat,set_Pr1986765409at_nat,X1,X3)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(nat,set_Pr1986765409at_nat,X1,vAPP(sTfun(nat,set_Pr1986765409at_nat),nat,sK147,X1))),vAPP(nat,set_Pr1986765409at_nat,X1,vAPP(sTfun(nat,set_Pr1986765409at_nat),nat,sK148,X1))) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X2),X3) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),vAPP(nat,set_Pr1986765409at_nat,X1,X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_312])]) ).
thf(f2475,plain,
! [X2: nat,X3: nat,X0: set_Pr1986765409at_nat,X1: nat > set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),vAPP(nat,set_Pr1986765409at_nat,X1,X3)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(nat,set_Pr1986765409at_nat,X1,vAPP(sTfun(nat,set_Pr1986765409at_nat),nat,sK147,X1))),vAPP(nat,set_Pr1986765409at_nat,X1,vAPP(sTfun(nat,set_Pr1986765409at_nat),nat,sK148,X1))) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X2),X3) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),vAPP(nat,set_Pr1986765409at_nat,X1,X2)) ) ),
inference(definition_unfolding,[],[f2072,f1656,f1656,f1646,f1656]) ).
thf(f2072,plain,
! [X2: nat,X3: nat,X0: set_Pr1986765409at_nat,X1: nat > set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),vAPP(nat,set_Pr1986765409at_nat,X1,X3)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(nat,set_Pr1986765409at_nat,X1,vAPP(sTfun(nat,set_Pr1986765409at_nat),nat,sK147,X1))),vAPP(nat,set_Pr1986765409at_nat,X1,vAPP(sTfun(nat,set_Pr1986765409at_nat),nat,sK148,X1))) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),vAPP(nat,set_Pr1986765409at_nat,X1,X2)) ) ),
inference(cnf_transformation,[],[f1608]) ).
thf(f1608,plain,
! [X0: set_Pr1986765409at_nat,X1: nat > set_Pr1986765409at_nat,X2: nat,X3: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),vAPP(nat,set_Pr1986765409at_nat,X1,X3)) )
| ( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(nat,set_Pr1986765409at_nat,X1,vAPP(sTfun(nat,set_Pr1986765409at_nat),nat,sK147,X1))),vAPP(nat,set_Pr1986765409at_nat,X1,vAPP(sTfun(nat,set_Pr1986765409at_nat),nat,sK148,X1))) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,set_Pr1986765409at_nat),nat,sK147,X1)),vAPP(sTfun(nat,set_Pr1986765409at_nat),nat,sK148,X1)) ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),vAPP(nat,set_Pr1986765409at_nat,X1,X2)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK147,sK148])],[f1406,f1607]) ).
thf(f1607,plain,
! [X1: nat > set_Pr1986765409at_nat] :
( ? [X4: nat,X5: nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(nat,set_Pr1986765409at_nat,X1,X4)),vAPP(nat,set_Pr1986765409at_nat,X1,X5)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) ) )
=> ( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(nat,set_Pr1986765409at_nat,X1,vAPP(sTfun(nat,set_Pr1986765409at_nat),nat,sK147,X1))),vAPP(nat,set_Pr1986765409at_nat,X1,vAPP(sTfun(nat,set_Pr1986765409at_nat),nat,sK148,X1))) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,set_Pr1986765409at_nat),nat,sK147,X1)),vAPP(sTfun(nat,set_Pr1986765409at_nat),nat,sK148,X1)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1406,plain,
! [X0: set_Pr1986765409at_nat,X1: nat > set_Pr1986765409at_nat,X2: nat,X3: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),vAPP(nat,set_Pr1986765409at_nat,X1,X3)) )
| ? [X4: nat,X5: nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(nat,set_Pr1986765409at_nat,X1,X4)),vAPP(nat,set_Pr1986765409at_nat,X1,X5)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),vAPP(nat,set_Pr1986765409at_nat,X1,X2)) ) ),
inference(flattening,[],[f1405]) ).
thf(f1405,plain,
! [X0: set_Pr1986765409at_nat,X1: nat > set_Pr1986765409at_nat,X2: nat,X3: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),vAPP(nat,set_Pr1986765409at_nat,X1,X3)) )
| ? [X4: nat,X5: nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(nat,set_Pr1986765409at_nat,X1,X4)),vAPP(nat,set_Pr1986765409at_nat,X1,X5)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),vAPP(nat,set_Pr1986765409at_nat,X1,X2)) ) ),
inference(ennf_transformation,[],[f987]) ).
thf(f987,plain,
! [X0: set_Pr1986765409at_nat,X1: nat > set_Pr1986765409at_nat,X2: nat,X3: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),vAPP(nat,set_Pr1986765409at_nat,X1,X2)) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
=> ( ! [X4: nat,X5: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) )
=> ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(nat,set_Pr1986765409at_nat,X1,X4)),vAPP(nat,set_Pr1986765409at_nat,X1,X5)) ) )
=> ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),vAPP(nat,set_Pr1986765409at_nat,X1,X3)) ) ) ) ),
inference(fool_elimination,[],[f986]) ).
thf(f986,plain,
! [X0: set_Pr1986765409at_nat,X1: nat > set_Pr1986765409at_nat,X2: nat,X3: nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),vAPP(nat,set_Pr1986765409at_nat,X1,X2))
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3)
=> ( ! [X4: nat,X5: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5)
=> vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(nat,set_Pr1986765409at_nat,X1,X4)),vAPP(nat,set_Pr1986765409at_nat,X1,X5)) )
=> vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),vAPP(nat,set_Pr1986765409at_nat,X1,X3)) ) ) ),
inference(rectify,[],[f108]) ).
thf(f108,axiom,
! [X13: set_Pr1986765409at_nat,X25: nat > set_Pr1986765409at_nat,X12: nat,X9: nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X13),vAPP(nat,set_Pr1986765409at_nat,X25,X12))
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X12),X9)
=> ( ! [X4: nat,X26: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X26)
=> vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(nat,set_Pr1986765409at_nat,X25,X4)),vAPP(nat,set_Pr1986765409at_nat,X25,X26)) )
=> vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X13),vAPP(nat,set_Pr1986765409at_nat,X25,X9)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_order__subst1) ).
thf(f6833,plain,
spl155_311,
inference(avatar_split_clause,[],[f2473,f6831]) ).
thf(f6831,plain,
( spl155_311
<=> ! [X0: set_Pr1986765409at_nat,X3: set_nat,X2: set_nat,X1: set_nat > set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),vAPP(set_nat,set_Pr1986765409at_nat,X1,X3)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_nat,set_Pr1986765409at_nat,X1,vAPP(sTfun(set_nat,set_Pr1986765409at_nat),set_nat,sK145,X1))),vAPP(set_nat,set_Pr1986765409at_nat,X1,vAPP(sTfun(set_nat,set_Pr1986765409at_nat),set_nat,sK146,X1))) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X2),X3) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),vAPP(set_nat,set_Pr1986765409at_nat,X1,X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_311])]) ).
thf(f2473,plain,
! [X2: set_nat,X3: set_nat,X0: set_Pr1986765409at_nat,X1: set_nat > set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),vAPP(set_nat,set_Pr1986765409at_nat,X1,X3)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_nat,set_Pr1986765409at_nat,X1,vAPP(sTfun(set_nat,set_Pr1986765409at_nat),set_nat,sK145,X1))),vAPP(set_nat,set_Pr1986765409at_nat,X1,vAPP(sTfun(set_nat,set_Pr1986765409at_nat),set_nat,sK146,X1))) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X2),X3) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),vAPP(set_nat,set_Pr1986765409at_nat,X1,X2)) ) ),
inference(definition_unfolding,[],[f2070,f1656,f1656,f1650,f1656]) ).
thf(f2070,plain,
! [X2: set_nat,X3: set_nat,X0: set_Pr1986765409at_nat,X1: set_nat > set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),vAPP(set_nat,set_Pr1986765409at_nat,X1,X3)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_nat,set_Pr1986765409at_nat,X1,vAPP(sTfun(set_nat,set_Pr1986765409at_nat),set_nat,sK145,X1))),vAPP(set_nat,set_Pr1986765409at_nat,X1,vAPP(sTfun(set_nat,set_Pr1986765409at_nat),set_nat,sK146,X1))) )
| ( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X3) != $true )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),vAPP(set_nat,set_Pr1986765409at_nat,X1,X2)) ) ),
inference(cnf_transformation,[],[f1606]) ).
thf(f1606,plain,
! [X0: set_Pr1986765409at_nat,X1: set_nat > set_Pr1986765409at_nat,X2: set_nat,X3: set_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),vAPP(set_nat,set_Pr1986765409at_nat,X1,X3)) )
| ( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_nat,set_Pr1986765409at_nat,X1,vAPP(sTfun(set_nat,set_Pr1986765409at_nat),set_nat,sK145,X1))),vAPP(set_nat,set_Pr1986765409at_nat,X1,vAPP(sTfun(set_nat,set_Pr1986765409at_nat),set_nat,sK146,X1))) )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(sTfun(set_nat,set_Pr1986765409at_nat),set_nat,sK145,X1)),vAPP(sTfun(set_nat,set_Pr1986765409at_nat),set_nat,sK146,X1)) ) )
| ( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X3) != $true )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),vAPP(set_nat,set_Pr1986765409at_nat,X1,X2)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK145,sK146])],[f1404,f1605]) ).
thf(f1605,plain,
! [X1: set_nat > set_Pr1986765409at_nat] :
( ? [X4: set_nat,X5: set_nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_nat,set_Pr1986765409at_nat,X1,X4)),vAPP(set_nat,set_Pr1986765409at_nat,X1,X5)) )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X4),X5) ) )
=> ( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_nat,set_Pr1986765409at_nat,X1,vAPP(sTfun(set_nat,set_Pr1986765409at_nat),set_nat,sK145,X1))),vAPP(set_nat,set_Pr1986765409at_nat,X1,vAPP(sTfun(set_nat,set_Pr1986765409at_nat),set_nat,sK146,X1))) )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(sTfun(set_nat,set_Pr1986765409at_nat),set_nat,sK145,X1)),vAPP(sTfun(set_nat,set_Pr1986765409at_nat),set_nat,sK146,X1)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1404,plain,
! [X0: set_Pr1986765409at_nat,X1: set_nat > set_Pr1986765409at_nat,X2: set_nat,X3: set_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),vAPP(set_nat,set_Pr1986765409at_nat,X1,X3)) )
| ? [X4: set_nat,X5: set_nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_nat,set_Pr1986765409at_nat,X1,X4)),vAPP(set_nat,set_Pr1986765409at_nat,X1,X5)) )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X4),X5) ) )
| ( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X3) != $true )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),vAPP(set_nat,set_Pr1986765409at_nat,X1,X2)) ) ),
inference(flattening,[],[f1403]) ).
thf(f1403,plain,
! [X0: set_Pr1986765409at_nat,X1: set_nat > set_Pr1986765409at_nat,X2: set_nat,X3: set_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),vAPP(set_nat,set_Pr1986765409at_nat,X1,X3)) )
| ? [X4: set_nat,X5: set_nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_nat,set_Pr1986765409at_nat,X1,X4)),vAPP(set_nat,set_Pr1986765409at_nat,X1,X5)) )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X4),X5) ) )
| ( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X3) != $true )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),vAPP(set_nat,set_Pr1986765409at_nat,X1,X2)) ) ),
inference(ennf_transformation,[],[f985]) ).
thf(f985,plain,
! [X0: set_Pr1986765409at_nat,X1: set_nat > set_Pr1986765409at_nat,X2: set_nat,X3: set_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),vAPP(set_nat,set_Pr1986765409at_nat,X1,X2)) )
=> ( ( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X3) = $true )
=> ( ! [X4: set_nat,X5: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X4),X5) )
=> ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_nat,set_Pr1986765409at_nat,X1,X4)),vAPP(set_nat,set_Pr1986765409at_nat,X1,X5)) ) )
=> ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),vAPP(set_nat,set_Pr1986765409at_nat,X1,X3)) ) ) ) ),
inference(fool_elimination,[],[f984]) ).
thf(f984,plain,
! [X0: set_Pr1986765409at_nat,X1: set_nat > set_Pr1986765409at_nat,X2: set_nat,X3: set_nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),vAPP(set_nat,set_Pr1986765409at_nat,X1,X2))
=> ( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X3)
=> ( ! [X4: set_nat,X5: set_nat] :
( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X4),X5)
=> vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_nat,set_Pr1986765409at_nat,X1,X4)),vAPP(set_nat,set_Pr1986765409at_nat,X1,X5)) )
=> vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),vAPP(set_nat,set_Pr1986765409at_nat,X1,X3)) ) ) ),
inference(rectify,[],[f107]) ).
thf(f107,axiom,
! [X13: set_Pr1986765409at_nat,X25: set_nat > set_Pr1986765409at_nat,X12: set_nat,X9: set_nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X13),vAPP(set_nat,set_Pr1986765409at_nat,X25,X12))
=> ( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X12),X9)
=> ( ! [X4: set_nat,X26: set_nat] :
( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X4),X26)
=> vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_nat,set_Pr1986765409at_nat,X25,X4)),vAPP(set_nat,set_Pr1986765409at_nat,X25,X26)) )
=> vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X13),vAPP(set_nat,set_Pr1986765409at_nat,X25,X9)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_order__subst1) ).
thf(f6829,plain,
spl155_310,
inference(avatar_split_clause,[],[f2471,f6827]) ).
thf(f6827,plain,
( spl155_310
<=> ! [X0: nat,X3: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat > nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),vAPP(set_Pr1986765409at_nat,nat,X1,X3)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,nat,X1,vAPP(sTfun(set_Pr1986765409at_nat,nat),set_Pr1986765409at_nat,sK143,X1))),vAPP(set_Pr1986765409at_nat,nat,X1,vAPP(sTfun(set_Pr1986765409at_nat,nat),set_Pr1986765409at_nat,sK144,X1))) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X2),X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),vAPP(set_Pr1986765409at_nat,nat,X1,X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_310])]) ).
thf(f2471,plain,
! [X2: set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat,X0: nat,X1: set_Pr1986765409at_nat > nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),vAPP(set_Pr1986765409at_nat,nat,X1,X3)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,nat,X1,vAPP(sTfun(set_Pr1986765409at_nat,nat),set_Pr1986765409at_nat,sK143,X1))),vAPP(set_Pr1986765409at_nat,nat,X1,vAPP(sTfun(set_Pr1986765409at_nat,nat),set_Pr1986765409at_nat,sK144,X1))) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X2),X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),vAPP(set_Pr1986765409at_nat,nat,X1,X2)) ) ),
inference(definition_unfolding,[],[f2068,f1646,f1646,f1656,f1646]) ).
thf(f2068,plain,
! [X2: set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat,X0: nat,X1: set_Pr1986765409at_nat > nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(set_Pr1986765409at_nat,nat,X1,X3)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,X1,vAPP(sTfun(set_Pr1986765409at_nat,nat),set_Pr1986765409at_nat,sK143,X1))),vAPP(set_Pr1986765409at_nat,nat,X1,vAPP(sTfun(set_Pr1986765409at_nat,nat),set_Pr1986765409at_nat,sK144,X1))) )
| ( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X2),X3) != $true )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(set_Pr1986765409at_nat,nat,X1,X2)) ) ),
inference(cnf_transformation,[],[f1604]) ).
thf(f1604,plain,
! [X0: nat,X1: set_Pr1986765409at_nat > nat,X2: set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(set_Pr1986765409at_nat,nat,X1,X3)) )
| ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,X1,vAPP(sTfun(set_Pr1986765409at_nat,nat),set_Pr1986765409at_nat,sK143,X1))),vAPP(set_Pr1986765409at_nat,nat,X1,vAPP(sTfun(set_Pr1986765409at_nat,nat),set_Pr1986765409at_nat,sK144,X1))) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(sTfun(set_Pr1986765409at_nat,nat),set_Pr1986765409at_nat,sK143,X1)),vAPP(sTfun(set_Pr1986765409at_nat,nat),set_Pr1986765409at_nat,sK144,X1)) ) )
| ( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X2),X3) != $true )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(set_Pr1986765409at_nat,nat,X1,X2)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK143,sK144])],[f1402,f1603]) ).
thf(f1603,plain,
! [X1: set_Pr1986765409at_nat > nat] :
( ? [X4: set_Pr1986765409at_nat,X5: set_Pr1986765409at_nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,X1,X4)),vAPP(set_Pr1986765409at_nat,nat,X1,X5)) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X4),X5) ) )
=> ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,X1,vAPP(sTfun(set_Pr1986765409at_nat,nat),set_Pr1986765409at_nat,sK143,X1))),vAPP(set_Pr1986765409at_nat,nat,X1,vAPP(sTfun(set_Pr1986765409at_nat,nat),set_Pr1986765409at_nat,sK144,X1))) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(sTfun(set_Pr1986765409at_nat,nat),set_Pr1986765409at_nat,sK143,X1)),vAPP(sTfun(set_Pr1986765409at_nat,nat),set_Pr1986765409at_nat,sK144,X1)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1402,plain,
! [X0: nat,X1: set_Pr1986765409at_nat > nat,X2: set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(set_Pr1986765409at_nat,nat,X1,X3)) )
| ? [X4: set_Pr1986765409at_nat,X5: set_Pr1986765409at_nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,X1,X4)),vAPP(set_Pr1986765409at_nat,nat,X1,X5)) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X4),X5) ) )
| ( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X2),X3) != $true )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(set_Pr1986765409at_nat,nat,X1,X2)) ) ),
inference(flattening,[],[f1401]) ).
thf(f1401,plain,
! [X0: nat,X1: set_Pr1986765409at_nat > nat,X2: set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(set_Pr1986765409at_nat,nat,X1,X3)) )
| ? [X4: set_Pr1986765409at_nat,X5: set_Pr1986765409at_nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,X1,X4)),vAPP(set_Pr1986765409at_nat,nat,X1,X5)) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X4),X5) ) )
| ( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X2),X3) != $true )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(set_Pr1986765409at_nat,nat,X1,X2)) ) ),
inference(ennf_transformation,[],[f983]) ).
thf(f983,plain,
! [X0: nat,X1: set_Pr1986765409at_nat > nat,X2: set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(set_Pr1986765409at_nat,nat,X1,X2)) )
=> ( ( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X2),X3) = $true )
=> ( ! [X4: set_Pr1986765409at_nat,X5: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X4),X5) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,X1,X4)),vAPP(set_Pr1986765409at_nat,nat,X1,X5)) ) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(set_Pr1986765409at_nat,nat,X1,X3)) ) ) ) ),
inference(fool_elimination,[],[f982]) ).
thf(f982,plain,
! [X0: nat,X1: set_Pr1986765409at_nat > nat,X2: set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(set_Pr1986765409at_nat,nat,X1,X2))
=> ( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X2),X3)
=> ( ! [X4: set_Pr1986765409at_nat,X5: set_Pr1986765409at_nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X4),X5)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,X1,X4)),vAPP(set_Pr1986765409at_nat,nat,X1,X5)) )
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(set_Pr1986765409at_nat,nat,X1,X3)) ) ) ),
inference(rectify,[],[f112]) ).
thf(f112,axiom,
! [X13: nat,X25: set_Pr1986765409at_nat > nat,X12: set_Pr1986765409at_nat,X9: set_Pr1986765409at_nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X13),vAPP(set_Pr1986765409at_nat,nat,X25,X12))
=> ( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X12),X9)
=> ( ! [X4: set_Pr1986765409at_nat,X26: set_Pr1986765409at_nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X4),X26)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,X25,X4)),vAPP(set_Pr1986765409at_nat,nat,X25,X26)) )
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X13),vAPP(set_Pr1986765409at_nat,nat,X25,X9)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_order__subst1) ).
thf(f6825,plain,
spl155_309,
inference(avatar_split_clause,[],[f2469,f6823]) ).
thf(f6823,plain,
( spl155_309
<=> ! [X0: nat,X3: nat,X2: nat,X1: nat > nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),vAPP(nat,nat,X1,X3)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(nat,nat,X1,vAPP(sTfun(nat,nat),nat,sK141,X1))),vAPP(nat,nat,X1,vAPP(sTfun(nat,nat),nat,sK142,X1))) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X2),X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),vAPP(nat,nat,X1,X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_309])]) ).
thf(f2469,plain,
! [X2: nat,X3: nat,X0: nat,X1: nat > nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),vAPP(nat,nat,X1,X3)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(nat,nat,X1,vAPP(sTfun(nat,nat),nat,sK141,X1))),vAPP(nat,nat,X1,vAPP(sTfun(nat,nat),nat,sK142,X1))) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X2),X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),vAPP(nat,nat,X1,X2)) ) ),
inference(definition_unfolding,[],[f2066,f1646,f1646,f1646,f1646]) ).
thf(f2066,plain,
! [X2: nat,X3: nat,X0: nat,X1: nat > nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,X1,X3)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X1,vAPP(sTfun(nat,nat),nat,sK141,X1))),vAPP(nat,nat,X1,vAPP(sTfun(nat,nat),nat,sK142,X1))) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,X1,X2)) ) ),
inference(cnf_transformation,[],[f1602]) ).
thf(f1602,plain,
! [X0: nat,X1: nat > nat,X2: nat,X3: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,X1,X3)) )
| ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X1,vAPP(sTfun(nat,nat),nat,sK141,X1))),vAPP(nat,nat,X1,vAPP(sTfun(nat,nat),nat,sK142,X1))) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,nat),nat,sK141,X1)),vAPP(sTfun(nat,nat),nat,sK142,X1)) ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,X1,X2)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK141,sK142])],[f1400,f1601]) ).
thf(f1601,plain,
! [X1: nat > nat] :
( ? [X4: nat,X5: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X1,X4)),vAPP(nat,nat,X1,X5)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) ) )
=> ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X1,vAPP(sTfun(nat,nat),nat,sK141,X1))),vAPP(nat,nat,X1,vAPP(sTfun(nat,nat),nat,sK142,X1))) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,nat),nat,sK141,X1)),vAPP(sTfun(nat,nat),nat,sK142,X1)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1400,plain,
! [X0: nat,X1: nat > nat,X2: nat,X3: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,X1,X3)) )
| ? [X4: nat,X5: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X1,X4)),vAPP(nat,nat,X1,X5)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,X1,X2)) ) ),
inference(flattening,[],[f1399]) ).
thf(f1399,plain,
! [X0: nat,X1: nat > nat,X2: nat,X3: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,X1,X3)) )
| ? [X4: nat,X5: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X1,X4)),vAPP(nat,nat,X1,X5)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,X1,X2)) ) ),
inference(ennf_transformation,[],[f981]) ).
thf(f981,plain,
! [X0: nat,X1: nat > nat,X2: nat,X3: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,X1,X2)) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
=> ( ! [X4: nat,X5: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X1,X4)),vAPP(nat,nat,X1,X5)) ) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,X1,X3)) ) ) ) ),
inference(fool_elimination,[],[f980]) ).
thf(f980,plain,
! [X0: nat,X1: nat > nat,X2: nat,X3: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,X1,X2))
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3)
=> ( ! [X4: nat,X5: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X1,X4)),vAPP(nat,nat,X1,X5)) )
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,X1,X3)) ) ) ),
inference(rectify,[],[f114]) ).
thf(f114,axiom,
! [X13: nat,X25: nat > nat,X12: nat,X9: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X13),vAPP(nat,nat,X25,X12))
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X12),X9)
=> ( ! [X4: nat,X26: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X26)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X25,X4)),vAPP(nat,nat,X25,X26)) )
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X13),vAPP(nat,nat,X25,X9)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_order__subst1) ).
thf(f6821,plain,
spl155_308,
inference(avatar_split_clause,[],[f2467,f6819]) ).
thf(f6819,plain,
( spl155_308
<=> ! [X0: nat,X3: set_nat,X2: set_nat,X1: set_nat > nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),vAPP(set_nat,nat,X1,X3)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_nat,nat,X1,vAPP(sTfun(set_nat,nat),set_nat,sK139,X1))),vAPP(set_nat,nat,X1,vAPP(sTfun(set_nat,nat),set_nat,sK140,X1))) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X2),X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),vAPP(set_nat,nat,X1,X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_308])]) ).
thf(f2467,plain,
! [X2: set_nat,X3: set_nat,X0: nat,X1: set_nat > nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),vAPP(set_nat,nat,X1,X3)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_nat,nat,X1,vAPP(sTfun(set_nat,nat),set_nat,sK139,X1))),vAPP(set_nat,nat,X1,vAPP(sTfun(set_nat,nat),set_nat,sK140,X1))) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X2),X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),vAPP(set_nat,nat,X1,X2)) ) ),
inference(definition_unfolding,[],[f2064,f1646,f1646,f1650,f1646]) ).
thf(f2064,plain,
! [X2: set_nat,X3: set_nat,X0: nat,X1: set_nat > nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(set_nat,nat,X1,X3)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,X1,vAPP(sTfun(set_nat,nat),set_nat,sK139,X1))),vAPP(set_nat,nat,X1,vAPP(sTfun(set_nat,nat),set_nat,sK140,X1))) )
| ( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X3) != $true )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(set_nat,nat,X1,X2)) ) ),
inference(cnf_transformation,[],[f1600]) ).
thf(f1600,plain,
! [X0: nat,X1: set_nat > nat,X2: set_nat,X3: set_nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(set_nat,nat,X1,X3)) )
| ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,X1,vAPP(sTfun(set_nat,nat),set_nat,sK139,X1))),vAPP(set_nat,nat,X1,vAPP(sTfun(set_nat,nat),set_nat,sK140,X1))) )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(sTfun(set_nat,nat),set_nat,sK139,X1)),vAPP(sTfun(set_nat,nat),set_nat,sK140,X1)) ) )
| ( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X3) != $true )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(set_nat,nat,X1,X2)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK139,sK140])],[f1398,f1599]) ).
thf(f1599,plain,
! [X1: set_nat > nat] :
( ? [X4: set_nat,X5: set_nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,X1,X4)),vAPP(set_nat,nat,X1,X5)) )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X4),X5) ) )
=> ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,X1,vAPP(sTfun(set_nat,nat),set_nat,sK139,X1))),vAPP(set_nat,nat,X1,vAPP(sTfun(set_nat,nat),set_nat,sK140,X1))) )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(sTfun(set_nat,nat),set_nat,sK139,X1)),vAPP(sTfun(set_nat,nat),set_nat,sK140,X1)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1398,plain,
! [X0: nat,X1: set_nat > nat,X2: set_nat,X3: set_nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(set_nat,nat,X1,X3)) )
| ? [X4: set_nat,X5: set_nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,X1,X4)),vAPP(set_nat,nat,X1,X5)) )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X4),X5) ) )
| ( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X3) != $true )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(set_nat,nat,X1,X2)) ) ),
inference(flattening,[],[f1397]) ).
thf(f1397,plain,
! [X0: nat,X1: set_nat > nat,X2: set_nat,X3: set_nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(set_nat,nat,X1,X3)) )
| ? [X4: set_nat,X5: set_nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,X1,X4)),vAPP(set_nat,nat,X1,X5)) )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X4),X5) ) )
| ( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X3) != $true )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(set_nat,nat,X1,X2)) ) ),
inference(ennf_transformation,[],[f979]) ).
thf(f979,plain,
! [X0: nat,X1: set_nat > nat,X2: set_nat,X3: set_nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(set_nat,nat,X1,X2)) )
=> ( ( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X3) = $true )
=> ( ! [X4: set_nat,X5: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X4),X5) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,X1,X4)),vAPP(set_nat,nat,X1,X5)) ) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(set_nat,nat,X1,X3)) ) ) ) ),
inference(fool_elimination,[],[f978]) ).
thf(f978,plain,
! [X0: nat,X1: set_nat > nat,X2: set_nat,X3: set_nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(set_nat,nat,X1,X2))
=> ( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X3)
=> ( ! [X4: set_nat,X5: set_nat] :
( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X4),X5)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,X1,X4)),vAPP(set_nat,nat,X1,X5)) )
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(set_nat,nat,X1,X3)) ) ) ),
inference(rectify,[],[f113]) ).
thf(f113,axiom,
! [X13: nat,X25: set_nat > nat,X12: set_nat,X9: set_nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X13),vAPP(set_nat,nat,X25,X12))
=> ( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X12),X9)
=> ( ! [X4: set_nat,X26: set_nat] :
( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X4),X26)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,X25,X4)),vAPP(set_nat,nat,X25,X26)) )
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X13),vAPP(set_nat,nat,X25,X9)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_order__subst1) ).
thf(f6811,plain,
spl155_307,
inference(avatar_split_clause,[],[f2465,f6809]) ).
thf(f6809,plain,
( spl155_307
<=> ! [X0: set_nat,X3: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat > set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),vAPP(set_Pr1986765409at_nat,set_nat,X1,X3)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_nat,X1,vAPP(sTfun(set_Pr1986765409at_nat,set_nat),set_Pr1986765409at_nat,sK137,X1))),vAPP(set_Pr1986765409at_nat,set_nat,X1,vAPP(sTfun(set_Pr1986765409at_nat,set_nat),set_Pr1986765409at_nat,sK138,X1))) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X2),X3) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),vAPP(set_Pr1986765409at_nat,set_nat,X1,X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_307])]) ).
thf(f2465,plain,
! [X2: set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat,X0: set_nat,X1: set_Pr1986765409at_nat > set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),vAPP(set_Pr1986765409at_nat,set_nat,X1,X3)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_nat,X1,vAPP(sTfun(set_Pr1986765409at_nat,set_nat),set_Pr1986765409at_nat,sK137,X1))),vAPP(set_Pr1986765409at_nat,set_nat,X1,vAPP(sTfun(set_Pr1986765409at_nat,set_nat),set_Pr1986765409at_nat,sK138,X1))) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X2),X3) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),vAPP(set_Pr1986765409at_nat,set_nat,X1,X2)) ) ),
inference(definition_unfolding,[],[f2062,f1650,f1650,f1656,f1650]) ).
thf(f2062,plain,
! [X2: set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat,X0: set_nat,X1: set_Pr1986765409at_nat > set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),vAPP(set_Pr1986765409at_nat,set_nat,X1,X3)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_Pr1986765409at_nat,set_nat,X1,vAPP(sTfun(set_Pr1986765409at_nat,set_nat),set_Pr1986765409at_nat,sK137,X1))),vAPP(set_Pr1986765409at_nat,set_nat,X1,vAPP(sTfun(set_Pr1986765409at_nat,set_nat),set_Pr1986765409at_nat,sK138,X1))) )
| ( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X2),X3) != $true )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),vAPP(set_Pr1986765409at_nat,set_nat,X1,X2)) ) ),
inference(cnf_transformation,[],[f1598]) ).
thf(f1598,plain,
! [X0: set_nat,X1: set_Pr1986765409at_nat > set_nat,X2: set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),vAPP(set_Pr1986765409at_nat,set_nat,X1,X3)) )
| ( ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_Pr1986765409at_nat,set_nat,X1,vAPP(sTfun(set_Pr1986765409at_nat,set_nat),set_Pr1986765409at_nat,sK137,X1))),vAPP(set_Pr1986765409at_nat,set_nat,X1,vAPP(sTfun(set_Pr1986765409at_nat,set_nat),set_Pr1986765409at_nat,sK138,X1))) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(sTfun(set_Pr1986765409at_nat,set_nat),set_Pr1986765409at_nat,sK137,X1)),vAPP(sTfun(set_Pr1986765409at_nat,set_nat),set_Pr1986765409at_nat,sK138,X1)) ) )
| ( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X2),X3) != $true )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),vAPP(set_Pr1986765409at_nat,set_nat,X1,X2)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK137,sK138])],[f1396,f1597]) ).
thf(f1597,plain,
! [X1: set_Pr1986765409at_nat > set_nat] :
( ? [X4: set_Pr1986765409at_nat,X5: set_Pr1986765409at_nat] :
( ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_Pr1986765409at_nat,set_nat,X1,X4)),vAPP(set_Pr1986765409at_nat,set_nat,X1,X5)) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X4),X5) ) )
=> ( ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_Pr1986765409at_nat,set_nat,X1,vAPP(sTfun(set_Pr1986765409at_nat,set_nat),set_Pr1986765409at_nat,sK137,X1))),vAPP(set_Pr1986765409at_nat,set_nat,X1,vAPP(sTfun(set_Pr1986765409at_nat,set_nat),set_Pr1986765409at_nat,sK138,X1))) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(sTfun(set_Pr1986765409at_nat,set_nat),set_Pr1986765409at_nat,sK137,X1)),vAPP(sTfun(set_Pr1986765409at_nat,set_nat),set_Pr1986765409at_nat,sK138,X1)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1396,plain,
! [X0: set_nat,X1: set_Pr1986765409at_nat > set_nat,X2: set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),vAPP(set_Pr1986765409at_nat,set_nat,X1,X3)) )
| ? [X4: set_Pr1986765409at_nat,X5: set_Pr1986765409at_nat] :
( ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_Pr1986765409at_nat,set_nat,X1,X4)),vAPP(set_Pr1986765409at_nat,set_nat,X1,X5)) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X4),X5) ) )
| ( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X2),X3) != $true )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),vAPP(set_Pr1986765409at_nat,set_nat,X1,X2)) ) ),
inference(flattening,[],[f1395]) ).
thf(f1395,plain,
! [X0: set_nat,X1: set_Pr1986765409at_nat > set_nat,X2: set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),vAPP(set_Pr1986765409at_nat,set_nat,X1,X3)) )
| ? [X4: set_Pr1986765409at_nat,X5: set_Pr1986765409at_nat] :
( ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_Pr1986765409at_nat,set_nat,X1,X4)),vAPP(set_Pr1986765409at_nat,set_nat,X1,X5)) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X4),X5) ) )
| ( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X2),X3) != $true )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),vAPP(set_Pr1986765409at_nat,set_nat,X1,X2)) ) ),
inference(ennf_transformation,[],[f977]) ).
thf(f977,plain,
! [X0: set_nat,X1: set_Pr1986765409at_nat > set_nat,X2: set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),vAPP(set_Pr1986765409at_nat,set_nat,X1,X2)) )
=> ( ( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X2),X3) = $true )
=> ( ! [X4: set_Pr1986765409at_nat,X5: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X4),X5) )
=> ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_Pr1986765409at_nat,set_nat,X1,X4)),vAPP(set_Pr1986765409at_nat,set_nat,X1,X5)) ) )
=> ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),vAPP(set_Pr1986765409at_nat,set_nat,X1,X3)) ) ) ) ),
inference(fool_elimination,[],[f976]) ).
thf(f976,plain,
! [X0: set_nat,X1: set_Pr1986765409at_nat > set_nat,X2: set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat] :
( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),vAPP(set_Pr1986765409at_nat,set_nat,X1,X2))
=> ( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X2),X3)
=> ( ! [X4: set_Pr1986765409at_nat,X5: set_Pr1986765409at_nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X4),X5)
=> vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_Pr1986765409at_nat,set_nat,X1,X4)),vAPP(set_Pr1986765409at_nat,set_nat,X1,X5)) )
=> vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),vAPP(set_Pr1986765409at_nat,set_nat,X1,X3)) ) ) ),
inference(rectify,[],[f109]) ).
thf(f109,axiom,
! [X13: set_nat,X25: set_Pr1986765409at_nat > set_nat,X12: set_Pr1986765409at_nat,X9: set_Pr1986765409at_nat] :
( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X13),vAPP(set_Pr1986765409at_nat,set_nat,X25,X12))
=> ( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X12),X9)
=> ( ! [X4: set_Pr1986765409at_nat,X26: set_Pr1986765409at_nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X4),X26)
=> vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_Pr1986765409at_nat,set_nat,X25,X4)),vAPP(set_Pr1986765409at_nat,set_nat,X25,X26)) )
=> vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X13),vAPP(set_Pr1986765409at_nat,set_nat,X25,X9)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_order__subst1) ).
thf(f6807,plain,
spl155_306,
inference(avatar_split_clause,[],[f2463,f6805]) ).
thf(f6805,plain,
( spl155_306
<=> ! [X0: set_nat,X3: nat,X2: nat,X1: nat > set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),vAPP(nat,set_nat,X1,X3)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(nat,set_nat,X1,vAPP(sTfun(nat,set_nat),nat,sK135,X1))),vAPP(nat,set_nat,X1,vAPP(sTfun(nat,set_nat),nat,sK136,X1))) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X2),X3) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),vAPP(nat,set_nat,X1,X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_306])]) ).
thf(f2463,plain,
! [X2: nat,X3: nat,X0: set_nat,X1: nat > set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),vAPP(nat,set_nat,X1,X3)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(nat,set_nat,X1,vAPP(sTfun(nat,set_nat),nat,sK135,X1))),vAPP(nat,set_nat,X1,vAPP(sTfun(nat,set_nat),nat,sK136,X1))) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X2),X3) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),vAPP(nat,set_nat,X1,X2)) ) ),
inference(definition_unfolding,[],[f2060,f1650,f1650,f1646,f1650]) ).
thf(f2060,plain,
! [X2: nat,X3: nat,X0: set_nat,X1: nat > set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),vAPP(nat,set_nat,X1,X3)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(nat,set_nat,X1,vAPP(sTfun(nat,set_nat),nat,sK135,X1))),vAPP(nat,set_nat,X1,vAPP(sTfun(nat,set_nat),nat,sK136,X1))) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),vAPP(nat,set_nat,X1,X2)) ) ),
inference(cnf_transformation,[],[f1596]) ).
thf(f1596,plain,
! [X0: set_nat,X1: nat > set_nat,X2: nat,X3: nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),vAPP(nat,set_nat,X1,X3)) )
| ( ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(nat,set_nat,X1,vAPP(sTfun(nat,set_nat),nat,sK135,X1))),vAPP(nat,set_nat,X1,vAPP(sTfun(nat,set_nat),nat,sK136,X1))) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,set_nat),nat,sK135,X1)),vAPP(sTfun(nat,set_nat),nat,sK136,X1)) ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),vAPP(nat,set_nat,X1,X2)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK135,sK136])],[f1394,f1595]) ).
thf(f1595,plain,
! [X1: nat > set_nat] :
( ? [X4: nat,X5: nat] :
( ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(nat,set_nat,X1,X4)),vAPP(nat,set_nat,X1,X5)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) ) )
=> ( ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(nat,set_nat,X1,vAPP(sTfun(nat,set_nat),nat,sK135,X1))),vAPP(nat,set_nat,X1,vAPP(sTfun(nat,set_nat),nat,sK136,X1))) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,set_nat),nat,sK135,X1)),vAPP(sTfun(nat,set_nat),nat,sK136,X1)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1394,plain,
! [X0: set_nat,X1: nat > set_nat,X2: nat,X3: nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),vAPP(nat,set_nat,X1,X3)) )
| ? [X4: nat,X5: nat] :
( ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(nat,set_nat,X1,X4)),vAPP(nat,set_nat,X1,X5)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),vAPP(nat,set_nat,X1,X2)) ) ),
inference(flattening,[],[f1393]) ).
thf(f1393,plain,
! [X0: set_nat,X1: nat > set_nat,X2: nat,X3: nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),vAPP(nat,set_nat,X1,X3)) )
| ? [X4: nat,X5: nat] :
( ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(nat,set_nat,X1,X4)),vAPP(nat,set_nat,X1,X5)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),vAPP(nat,set_nat,X1,X2)) ) ),
inference(ennf_transformation,[],[f975]) ).
thf(f975,plain,
! [X0: set_nat,X1: nat > set_nat,X2: nat,X3: nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),vAPP(nat,set_nat,X1,X2)) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
=> ( ! [X4: nat,X5: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) )
=> ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(nat,set_nat,X1,X4)),vAPP(nat,set_nat,X1,X5)) ) )
=> ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),vAPP(nat,set_nat,X1,X3)) ) ) ) ),
inference(fool_elimination,[],[f974]) ).
thf(f974,plain,
! [X0: set_nat,X1: nat > set_nat,X2: nat,X3: nat] :
( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),vAPP(nat,set_nat,X1,X2))
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3)
=> ( ! [X4: nat,X5: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5)
=> vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(nat,set_nat,X1,X4)),vAPP(nat,set_nat,X1,X5)) )
=> vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),vAPP(nat,set_nat,X1,X3)) ) ) ),
inference(rectify,[],[f111]) ).
thf(f111,axiom,
! [X13: set_nat,X25: nat > set_nat,X12: nat,X9: nat] :
( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X13),vAPP(nat,set_nat,X25,X12))
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X12),X9)
=> ( ! [X4: nat,X26: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X26)
=> vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(nat,set_nat,X25,X4)),vAPP(nat,set_nat,X25,X26)) )
=> vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X13),vAPP(nat,set_nat,X25,X9)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_order__subst1) ).
thf(f6803,plain,
spl155_305,
inference(avatar_split_clause,[],[f2461,f6801]) ).
thf(f6801,plain,
( spl155_305
<=> ! [X0: set_nat,X3: set_nat,X2: set_nat,X1: set_nat > set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),vAPP(set_nat,set_nat,X1,X3)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_nat,set_nat,X1,vAPP(sTfun(set_nat,set_nat),set_nat,sK133,X1))),vAPP(set_nat,set_nat,X1,vAPP(sTfun(set_nat,set_nat),set_nat,sK134,X1))) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X2),X3) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),vAPP(set_nat,set_nat,X1,X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_305])]) ).
thf(f2461,plain,
! [X2: set_nat,X3: set_nat,X0: set_nat,X1: set_nat > set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),vAPP(set_nat,set_nat,X1,X3)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_nat,set_nat,X1,vAPP(sTfun(set_nat,set_nat),set_nat,sK133,X1))),vAPP(set_nat,set_nat,X1,vAPP(sTfun(set_nat,set_nat),set_nat,sK134,X1))) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X2),X3) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),vAPP(set_nat,set_nat,X1,X2)) ) ),
inference(definition_unfolding,[],[f2058,f1650,f1650,f1650,f1650]) ).
thf(f2058,plain,
! [X2: set_nat,X3: set_nat,X0: set_nat,X1: set_nat > set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),vAPP(set_nat,set_nat,X1,X3)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,X1,vAPP(sTfun(set_nat,set_nat),set_nat,sK133,X1))),vAPP(set_nat,set_nat,X1,vAPP(sTfun(set_nat,set_nat),set_nat,sK134,X1))) )
| ( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X3) != $true )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),vAPP(set_nat,set_nat,X1,X2)) ) ),
inference(cnf_transformation,[],[f1594]) ).
thf(f1594,plain,
! [X0: set_nat,X1: set_nat > set_nat,X2: set_nat,X3: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),vAPP(set_nat,set_nat,X1,X3)) )
| ( ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,X1,vAPP(sTfun(set_nat,set_nat),set_nat,sK133,X1))),vAPP(set_nat,set_nat,X1,vAPP(sTfun(set_nat,set_nat),set_nat,sK134,X1))) )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(sTfun(set_nat,set_nat),set_nat,sK133,X1)),vAPP(sTfun(set_nat,set_nat),set_nat,sK134,X1)) ) )
| ( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X3) != $true )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),vAPP(set_nat,set_nat,X1,X2)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK133,sK134])],[f1392,f1593]) ).
thf(f1593,plain,
! [X1: set_nat > set_nat] :
( ? [X4: set_nat,X5: set_nat] :
( ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,X1,X4)),vAPP(set_nat,set_nat,X1,X5)) )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X4),X5) ) )
=> ( ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,X1,vAPP(sTfun(set_nat,set_nat),set_nat,sK133,X1))),vAPP(set_nat,set_nat,X1,vAPP(sTfun(set_nat,set_nat),set_nat,sK134,X1))) )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(sTfun(set_nat,set_nat),set_nat,sK133,X1)),vAPP(sTfun(set_nat,set_nat),set_nat,sK134,X1)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1392,plain,
! [X0: set_nat,X1: set_nat > set_nat,X2: set_nat,X3: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),vAPP(set_nat,set_nat,X1,X3)) )
| ? [X4: set_nat,X5: set_nat] :
( ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,X1,X4)),vAPP(set_nat,set_nat,X1,X5)) )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X4),X5) ) )
| ( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X3) != $true )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),vAPP(set_nat,set_nat,X1,X2)) ) ),
inference(flattening,[],[f1391]) ).
thf(f1391,plain,
! [X0: set_nat,X1: set_nat > set_nat,X2: set_nat,X3: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),vAPP(set_nat,set_nat,X1,X3)) )
| ? [X4: set_nat,X5: set_nat] :
( ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,X1,X4)),vAPP(set_nat,set_nat,X1,X5)) )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X4),X5) ) )
| ( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X3) != $true )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),vAPP(set_nat,set_nat,X1,X2)) ) ),
inference(ennf_transformation,[],[f973]) ).
thf(f973,plain,
! [X0: set_nat,X1: set_nat > set_nat,X2: set_nat,X3: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),vAPP(set_nat,set_nat,X1,X2)) )
=> ( ( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X3) = $true )
=> ( ! [X4: set_nat,X5: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X4),X5) )
=> ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,X1,X4)),vAPP(set_nat,set_nat,X1,X5)) ) )
=> ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),vAPP(set_nat,set_nat,X1,X3)) ) ) ) ),
inference(fool_elimination,[],[f972]) ).
thf(f972,plain,
! [X0: set_nat,X1: set_nat > set_nat,X2: set_nat,X3: set_nat] :
( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),vAPP(set_nat,set_nat,X1,X2))
=> ( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X3)
=> ( ! [X4: set_nat,X5: set_nat] :
( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X4),X5)
=> vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,X1,X4)),vAPP(set_nat,set_nat,X1,X5)) )
=> vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),vAPP(set_nat,set_nat,X1,X3)) ) ) ),
inference(rectify,[],[f110]) ).
thf(f110,axiom,
! [X13: set_nat,X25: set_nat > set_nat,X12: set_nat,X9: set_nat] :
( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X13),vAPP(set_nat,set_nat,X25,X12))
=> ( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X12),X9)
=> ( ! [X4: set_nat,X26: set_nat] :
( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X4),X26)
=> vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,X25,X4)),vAPP(set_nat,set_nat,X25,X26)) )
=> vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X13),vAPP(set_nat,set_nat,X25,X9)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_order__subst1) ).
thf(f6799,plain,
spl155_304,
inference(avatar_split_clause,[],[f2459,f6797]) ).
thf(f6797,plain,
( spl155_304
<=> ! [X0: set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat > set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X2,X0)),X3) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X2,vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),set_Pr1986765409at_nat,sK131,X2))),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X2,vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),set_Pr1986765409at_nat,sK132,X2))) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X2,X1)),X3) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_304])]) ).
thf(f2459,plain,
! [X2: set_Pr1986765409at_nat > set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X2,X0)),X3) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X2,vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),set_Pr1986765409at_nat,sK131,X2))),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X2,vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),set_Pr1986765409at_nat,sK132,X2))) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X2,X1)),X3) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X1) ) ),
inference(definition_unfolding,[],[f2056,f1656,f1656,f1656,f1656]) ).
thf(f2056,plain,
! [X2: set_Pr1986765409at_nat > set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X2,X0)),X3) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X2,vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),set_Pr1986765409at_nat,sK131,X2))),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X2,vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),set_Pr1986765409at_nat,sK132,X2))) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X2,X1)),X3) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1592]) ).
thf(f1592,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat > set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X2,X0)),X3) )
| ( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X2,vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),set_Pr1986765409at_nat,sK131,X2))),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X2,vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),set_Pr1986765409at_nat,sK132,X2))) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),set_Pr1986765409at_nat,sK131,X2)),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),set_Pr1986765409at_nat,sK132,X2)) ) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X2,X1)),X3) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK131,sK132])],[f1390,f1591]) ).
thf(f1591,plain,
! [X2: set_Pr1986765409at_nat > set_Pr1986765409at_nat] :
( ? [X4: set_Pr1986765409at_nat,X5: set_Pr1986765409at_nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X2,X4)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X2,X5)) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X4),X5) ) )
=> ( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X2,vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),set_Pr1986765409at_nat,sK131,X2))),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X2,vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),set_Pr1986765409at_nat,sK132,X2))) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),set_Pr1986765409at_nat,sK131,X2)),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),set_Pr1986765409at_nat,sK132,X2)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1390,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat > set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X2,X0)),X3) )
| ? [X4: set_Pr1986765409at_nat,X5: set_Pr1986765409at_nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X2,X4)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X2,X5)) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X4),X5) ) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X2,X1)),X3) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1) ) ),
inference(flattening,[],[f1389]) ).
thf(f1389,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat > set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X2,X0)),X3) )
| ? [X4: set_Pr1986765409at_nat,X5: set_Pr1986765409at_nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X2,X4)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X2,X5)) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X4),X5) ) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X2,X1)),X3) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1) ) ),
inference(ennf_transformation,[],[f971]) ).
thf(f971,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat > set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1) )
=> ( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X2,X1)),X3) )
=> ( ! [X4: set_Pr1986765409at_nat,X5: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X4),X5) )
=> ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X2,X4)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X2,X5)) ) )
=> ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X2,X0)),X3) ) ) ) ),
inference(fool_elimination,[],[f970]) ).
thf(f970,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat > set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1)
=> ( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X2,X1)),X3)
=> ( ! [X4: set_Pr1986765409at_nat,X5: set_Pr1986765409at_nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X4),X5)
=> vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X2,X4)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X2,X5)) )
=> vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X2,X0)),X3) ) ) ),
inference(rectify,[],[f93]) ).
thf(f93,axiom,
! [X13: set_Pr1986765409at_nat,X12: set_Pr1986765409at_nat,X25: set_Pr1986765409at_nat > set_Pr1986765409at_nat,X9: set_Pr1986765409at_nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X13),X12)
=> ( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X25,X12)),X9)
=> ( ! [X4: set_Pr1986765409at_nat,X26: set_Pr1986765409at_nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X4),X26)
=> vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X25,X4)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X25,X26)) )
=> vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X25,X13)),X9) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_order__subst2) ).
thf(f6795,plain,
spl155_303,
inference(avatar_split_clause,[],[f2457,f6793]) ).
thf(f6793,plain,
( spl155_303
<=> ! [X0: set_Pr1986765409at_nat,X3: nat,X2: set_Pr1986765409at_nat > nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,nat,X2,X0)),X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,nat,X2,vAPP(sTfun(set_Pr1986765409at_nat,nat),set_Pr1986765409at_nat,sK129,X2))),vAPP(set_Pr1986765409at_nat,nat,X2,vAPP(sTfun(set_Pr1986765409at_nat,nat),set_Pr1986765409at_nat,sK130,X2))) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,nat,X2,X1)),X3) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_303])]) ).
thf(f2457,plain,
! [X2: set_Pr1986765409at_nat > nat,X3: nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,nat,X2,X0)),X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,nat,X2,vAPP(sTfun(set_Pr1986765409at_nat,nat),set_Pr1986765409at_nat,sK129,X2))),vAPP(set_Pr1986765409at_nat,nat,X2,vAPP(sTfun(set_Pr1986765409at_nat,nat),set_Pr1986765409at_nat,sK130,X2))) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,nat,X2,X1)),X3) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X1) ) ),
inference(definition_unfolding,[],[f2054,f1646,f1646,f1646,f1656]) ).
thf(f2054,plain,
! [X2: set_Pr1986765409at_nat > nat,X3: nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,X2,X0)),X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,X2,vAPP(sTfun(set_Pr1986765409at_nat,nat),set_Pr1986765409at_nat,sK129,X2))),vAPP(set_Pr1986765409at_nat,nat,X2,vAPP(sTfun(set_Pr1986765409at_nat,nat),set_Pr1986765409at_nat,sK130,X2))) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,X2,X1)),X3) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1590]) ).
thf(f1590,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat > nat,X3: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,X2,X0)),X3) )
| ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,X2,vAPP(sTfun(set_Pr1986765409at_nat,nat),set_Pr1986765409at_nat,sK129,X2))),vAPP(set_Pr1986765409at_nat,nat,X2,vAPP(sTfun(set_Pr1986765409at_nat,nat),set_Pr1986765409at_nat,sK130,X2))) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(sTfun(set_Pr1986765409at_nat,nat),set_Pr1986765409at_nat,sK129,X2)),vAPP(sTfun(set_Pr1986765409at_nat,nat),set_Pr1986765409at_nat,sK130,X2)) ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,X2,X1)),X3) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK129,sK130])],[f1388,f1589]) ).
thf(f1589,plain,
! [X2: set_Pr1986765409at_nat > nat] :
( ? [X4: set_Pr1986765409at_nat,X5: set_Pr1986765409at_nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,X2,X4)),vAPP(set_Pr1986765409at_nat,nat,X2,X5)) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X4),X5) ) )
=> ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,X2,vAPP(sTfun(set_Pr1986765409at_nat,nat),set_Pr1986765409at_nat,sK129,X2))),vAPP(set_Pr1986765409at_nat,nat,X2,vAPP(sTfun(set_Pr1986765409at_nat,nat),set_Pr1986765409at_nat,sK130,X2))) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(sTfun(set_Pr1986765409at_nat,nat),set_Pr1986765409at_nat,sK129,X2)),vAPP(sTfun(set_Pr1986765409at_nat,nat),set_Pr1986765409at_nat,sK130,X2)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1388,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat > nat,X3: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,X2,X0)),X3) )
| ? [X4: set_Pr1986765409at_nat,X5: set_Pr1986765409at_nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,X2,X4)),vAPP(set_Pr1986765409at_nat,nat,X2,X5)) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X4),X5) ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,X2,X1)),X3) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1) ) ),
inference(flattening,[],[f1387]) ).
thf(f1387,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat > nat,X3: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,X2,X0)),X3) )
| ? [X4: set_Pr1986765409at_nat,X5: set_Pr1986765409at_nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,X2,X4)),vAPP(set_Pr1986765409at_nat,nat,X2,X5)) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X4),X5) ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,X2,X1)),X3) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1) ) ),
inference(ennf_transformation,[],[f969]) ).
thf(f969,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat > nat,X3: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,X2,X1)),X3) )
=> ( ! [X4: set_Pr1986765409at_nat,X5: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X4),X5) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,X2,X4)),vAPP(set_Pr1986765409at_nat,nat,X2,X5)) ) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,X2,X0)),X3) ) ) ) ),
inference(fool_elimination,[],[f968]) ).
thf(f968,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat > nat,X3: nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,X2,X1)),X3)
=> ( ! [X4: set_Pr1986765409at_nat,X5: set_Pr1986765409at_nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X4),X5)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,X2,X4)),vAPP(set_Pr1986765409at_nat,nat,X2,X5)) )
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,X2,X0)),X3) ) ) ),
inference(rectify,[],[f95]) ).
thf(f95,axiom,
! [X13: set_Pr1986765409at_nat,X12: set_Pr1986765409at_nat,X25: set_Pr1986765409at_nat > nat,X9: nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X13),X12)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,X25,X12)),X9)
=> ( ! [X4: set_Pr1986765409at_nat,X26: set_Pr1986765409at_nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X4),X26)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,X25,X4)),vAPP(set_Pr1986765409at_nat,nat,X25,X26)) )
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,X25,X13)),X9) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_order__subst2) ).
thf(f6791,plain,
spl155_302,
inference(avatar_split_clause,[],[f2455,f6789]) ).
thf(f6789,plain,
( spl155_302
<=> ! [X0: set_Pr1986765409at_nat,X3: set_nat,X2: set_Pr1986765409at_nat > set_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_nat,X2,X0)),X3) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_nat,X2,vAPP(sTfun(set_Pr1986765409at_nat,set_nat),set_Pr1986765409at_nat,sK127,X2))),vAPP(set_Pr1986765409at_nat,set_nat,X2,vAPP(sTfun(set_Pr1986765409at_nat,set_nat),set_Pr1986765409at_nat,sK128,X2))) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_nat,X2,X1)),X3) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_302])]) ).
thf(f2455,plain,
! [X2: set_Pr1986765409at_nat > set_nat,X3: set_nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_nat,X2,X0)),X3) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_nat,X2,vAPP(sTfun(set_Pr1986765409at_nat,set_nat),set_Pr1986765409at_nat,sK127,X2))),vAPP(set_Pr1986765409at_nat,set_nat,X2,vAPP(sTfun(set_Pr1986765409at_nat,set_nat),set_Pr1986765409at_nat,sK128,X2))) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_nat,X2,X1)),X3) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X1) ) ),
inference(definition_unfolding,[],[f2052,f1650,f1650,f1650,f1656]) ).
thf(f2052,plain,
! [X2: set_Pr1986765409at_nat > set_nat,X3: set_nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_Pr1986765409at_nat,set_nat,X2,X0)),X3) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_Pr1986765409at_nat,set_nat,X2,vAPP(sTfun(set_Pr1986765409at_nat,set_nat),set_Pr1986765409at_nat,sK127,X2))),vAPP(set_Pr1986765409at_nat,set_nat,X2,vAPP(sTfun(set_Pr1986765409at_nat,set_nat),set_Pr1986765409at_nat,sK128,X2))) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_Pr1986765409at_nat,set_nat,X2,X1)),X3) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1588]) ).
thf(f1588,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat > set_nat,X3: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_Pr1986765409at_nat,set_nat,X2,X0)),X3) )
| ( ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_Pr1986765409at_nat,set_nat,X2,vAPP(sTfun(set_Pr1986765409at_nat,set_nat),set_Pr1986765409at_nat,sK127,X2))),vAPP(set_Pr1986765409at_nat,set_nat,X2,vAPP(sTfun(set_Pr1986765409at_nat,set_nat),set_Pr1986765409at_nat,sK128,X2))) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(sTfun(set_Pr1986765409at_nat,set_nat),set_Pr1986765409at_nat,sK127,X2)),vAPP(sTfun(set_Pr1986765409at_nat,set_nat),set_Pr1986765409at_nat,sK128,X2)) ) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_Pr1986765409at_nat,set_nat,X2,X1)),X3) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK127,sK128])],[f1386,f1587]) ).
thf(f1587,plain,
! [X2: set_Pr1986765409at_nat > set_nat] :
( ? [X4: set_Pr1986765409at_nat,X5: set_Pr1986765409at_nat] :
( ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_Pr1986765409at_nat,set_nat,X2,X4)),vAPP(set_Pr1986765409at_nat,set_nat,X2,X5)) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X4),X5) ) )
=> ( ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_Pr1986765409at_nat,set_nat,X2,vAPP(sTfun(set_Pr1986765409at_nat,set_nat),set_Pr1986765409at_nat,sK127,X2))),vAPP(set_Pr1986765409at_nat,set_nat,X2,vAPP(sTfun(set_Pr1986765409at_nat,set_nat),set_Pr1986765409at_nat,sK128,X2))) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(sTfun(set_Pr1986765409at_nat,set_nat),set_Pr1986765409at_nat,sK127,X2)),vAPP(sTfun(set_Pr1986765409at_nat,set_nat),set_Pr1986765409at_nat,sK128,X2)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1386,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat > set_nat,X3: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_Pr1986765409at_nat,set_nat,X2,X0)),X3) )
| ? [X4: set_Pr1986765409at_nat,X5: set_Pr1986765409at_nat] :
( ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_Pr1986765409at_nat,set_nat,X2,X4)),vAPP(set_Pr1986765409at_nat,set_nat,X2,X5)) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X4),X5) ) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_Pr1986765409at_nat,set_nat,X2,X1)),X3) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1) ) ),
inference(flattening,[],[f1385]) ).
thf(f1385,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat > set_nat,X3: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_Pr1986765409at_nat,set_nat,X2,X0)),X3) )
| ? [X4: set_Pr1986765409at_nat,X5: set_Pr1986765409at_nat] :
( ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_Pr1986765409at_nat,set_nat,X2,X4)),vAPP(set_Pr1986765409at_nat,set_nat,X2,X5)) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X4),X5) ) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_Pr1986765409at_nat,set_nat,X2,X1)),X3) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1) ) ),
inference(ennf_transformation,[],[f967]) ).
thf(f967,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat > set_nat,X3: set_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1) )
=> ( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_Pr1986765409at_nat,set_nat,X2,X1)),X3) )
=> ( ! [X4: set_Pr1986765409at_nat,X5: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X4),X5) )
=> ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_Pr1986765409at_nat,set_nat,X2,X4)),vAPP(set_Pr1986765409at_nat,set_nat,X2,X5)) ) )
=> ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_Pr1986765409at_nat,set_nat,X2,X0)),X3) ) ) ) ),
inference(fool_elimination,[],[f966]) ).
thf(f966,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat > set_nat,X3: set_nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1)
=> ( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_Pr1986765409at_nat,set_nat,X2,X1)),X3)
=> ( ! [X4: set_Pr1986765409at_nat,X5: set_Pr1986765409at_nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X4),X5)
=> vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_Pr1986765409at_nat,set_nat,X2,X4)),vAPP(set_Pr1986765409at_nat,set_nat,X2,X5)) )
=> vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_Pr1986765409at_nat,set_nat,X2,X0)),X3) ) ) ),
inference(rectify,[],[f94]) ).
thf(f94,axiom,
! [X13: set_Pr1986765409at_nat,X12: set_Pr1986765409at_nat,X25: set_Pr1986765409at_nat > set_nat,X9: set_nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X13),X12)
=> ( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_Pr1986765409at_nat,set_nat,X25,X12)),X9)
=> ( ! [X4: set_Pr1986765409at_nat,X26: set_Pr1986765409at_nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X4),X26)
=> vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_Pr1986765409at_nat,set_nat,X25,X4)),vAPP(set_Pr1986765409at_nat,set_nat,X25,X26)) )
=> vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_Pr1986765409at_nat,set_nat,X25,X13)),X9) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_order__subst2) ).
thf(f6787,plain,
spl155_301,
inference(avatar_split_clause,[],[f2442,f6785]) ).
thf(f6785,plain,
( spl155_301
<=> ! [X0: nat,X3: set_Pr1986765409at_nat,X2: nat > set_Pr1986765409at_nat,X1: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(nat,set_Pr1986765409at_nat,X2,X0)),X3) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(nat,set_Pr1986765409at_nat,X2,vAPP(sTfun(nat,set_Pr1986765409at_nat),nat,sK118,X2))),vAPP(nat,set_Pr1986765409at_nat,X2,vAPP(sTfun(nat,set_Pr1986765409at_nat),nat,sK119,X2))) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(nat,set_Pr1986765409at_nat,X2,X1)),X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_301])]) ).
thf(f2442,plain,
! [X2: nat > set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat,X0: nat,X1: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(nat,set_Pr1986765409at_nat,X2,X0)),X3) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(nat,set_Pr1986765409at_nat,X2,vAPP(sTfun(nat,set_Pr1986765409at_nat),nat,sK118,X2))),vAPP(nat,set_Pr1986765409at_nat,X2,vAPP(sTfun(nat,set_Pr1986765409at_nat),nat,sK119,X2))) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(nat,set_Pr1986765409at_nat,X2,X1)),X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),X1) ) ),
inference(definition_unfolding,[],[f2039,f1656,f1656,f1656,f1646]) ).
thf(f2039,plain,
! [X2: nat > set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat,X0: nat,X1: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(nat,set_Pr1986765409at_nat,X2,X0)),X3) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(nat,set_Pr1986765409at_nat,X2,vAPP(sTfun(nat,set_Pr1986765409at_nat),nat,sK118,X2))),vAPP(nat,set_Pr1986765409at_nat,X2,vAPP(sTfun(nat,set_Pr1986765409at_nat),nat,sK119,X2))) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(nat,set_Pr1986765409at_nat,X2,X1)),X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1578]) ).
thf(f1578,plain,
! [X0: nat,X1: nat,X2: nat > set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(nat,set_Pr1986765409at_nat,X2,X0)),X3) )
| ( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(nat,set_Pr1986765409at_nat,X2,vAPP(sTfun(nat,set_Pr1986765409at_nat),nat,sK118,X2))),vAPP(nat,set_Pr1986765409at_nat,X2,vAPP(sTfun(nat,set_Pr1986765409at_nat),nat,sK119,X2))) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,set_Pr1986765409at_nat),nat,sK118,X2)),vAPP(sTfun(nat,set_Pr1986765409at_nat),nat,sK119,X2)) ) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(nat,set_Pr1986765409at_nat,X2,X1)),X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK118,sK119])],[f1372,f1577]) ).
thf(f1577,plain,
! [X2: nat > set_Pr1986765409at_nat] :
( ? [X4: nat,X5: nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(nat,set_Pr1986765409at_nat,X2,X4)),vAPP(nat,set_Pr1986765409at_nat,X2,X5)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) ) )
=> ( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(nat,set_Pr1986765409at_nat,X2,vAPP(sTfun(nat,set_Pr1986765409at_nat),nat,sK118,X2))),vAPP(nat,set_Pr1986765409at_nat,X2,vAPP(sTfun(nat,set_Pr1986765409at_nat),nat,sK119,X2))) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,set_Pr1986765409at_nat),nat,sK118,X2)),vAPP(sTfun(nat,set_Pr1986765409at_nat),nat,sK119,X2)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1372,plain,
! [X0: nat,X1: nat,X2: nat > set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(nat,set_Pr1986765409at_nat,X2,X0)),X3) )
| ? [X4: nat,X5: nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(nat,set_Pr1986765409at_nat,X2,X4)),vAPP(nat,set_Pr1986765409at_nat,X2,X5)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) ) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(nat,set_Pr1986765409at_nat,X2,X1)),X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(flattening,[],[f1371]) ).
thf(f1371,plain,
! [X0: nat,X1: nat,X2: nat > set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(nat,set_Pr1986765409at_nat,X2,X0)),X3) )
| ? [X4: nat,X5: nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(nat,set_Pr1986765409at_nat,X2,X4)),vAPP(nat,set_Pr1986765409at_nat,X2,X5)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) ) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(nat,set_Pr1986765409at_nat,X2,X1)),X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(ennf_transformation,[],[f953]) ).
thf(f953,plain,
! [X0: nat,X1: nat,X2: nat > set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
=> ( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(nat,set_Pr1986765409at_nat,X2,X1)),X3) )
=> ( ! [X4: nat,X5: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) )
=> ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(nat,set_Pr1986765409at_nat,X2,X4)),vAPP(nat,set_Pr1986765409at_nat,X2,X5)) ) )
=> ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(nat,set_Pr1986765409at_nat,X2,X0)),X3) ) ) ) ),
inference(fool_elimination,[],[f952]) ).
thf(f952,plain,
! [X0: nat,X1: nat,X2: nat > set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1)
=> ( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(nat,set_Pr1986765409at_nat,X2,X1)),X3)
=> ( ! [X4: nat,X5: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5)
=> vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(nat,set_Pr1986765409at_nat,X2,X4)),vAPP(nat,set_Pr1986765409at_nat,X2,X5)) )
=> vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(nat,set_Pr1986765409at_nat,X2,X0)),X3) ) ) ),
inference(rectify,[],[f99]) ).
thf(f99,axiom,
! [X13: nat,X12: nat,X25: nat > set_Pr1986765409at_nat,X9: set_Pr1986765409at_nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X13),X12)
=> ( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(nat,set_Pr1986765409at_nat,X25,X12)),X9)
=> ( ! [X4: nat,X26: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X26)
=> vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(nat,set_Pr1986765409at_nat,X25,X4)),vAPP(nat,set_Pr1986765409at_nat,X25,X26)) )
=> vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(nat,set_Pr1986765409at_nat,X25,X13)),X9) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_order__subst2) ).
thf(f6783,plain,
spl155_300,
inference(avatar_split_clause,[],[f2440,f6781]) ).
thf(f6781,plain,
( spl155_300
<=> ! [X0: nat,X3: nat,X2: nat > nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(nat,nat,X2,X0)),X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(nat,nat,X2,vAPP(sTfun(nat,nat),nat,sK116,X2))),vAPP(nat,nat,X2,vAPP(sTfun(nat,nat),nat,sK117,X2))) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(nat,nat,X2,X1)),X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_300])]) ).
thf(f2440,plain,
! [X2: nat > nat,X3: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(nat,nat,X2,X0)),X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(nat,nat,X2,vAPP(sTfun(nat,nat),nat,sK116,X2))),vAPP(nat,nat,X2,vAPP(sTfun(nat,nat),nat,sK117,X2))) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(nat,nat,X2,X1)),X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),X1) ) ),
inference(definition_unfolding,[],[f2037,f1646,f1646,f1646,f1646]) ).
thf(f2037,plain,
! [X2: nat > nat,X3: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,X0)),X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,vAPP(sTfun(nat,nat),nat,sK116,X2))),vAPP(nat,nat,X2,vAPP(sTfun(nat,nat),nat,sK117,X2))) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,X1)),X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1576]) ).
thf(f1576,plain,
! [X0: nat,X1: nat,X2: nat > nat,X3: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,X0)),X3) )
| ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,vAPP(sTfun(nat,nat),nat,sK116,X2))),vAPP(nat,nat,X2,vAPP(sTfun(nat,nat),nat,sK117,X2))) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,nat),nat,sK116,X2)),vAPP(sTfun(nat,nat),nat,sK117,X2)) ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,X1)),X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK116,sK117])],[f1370,f1575]) ).
thf(f1575,plain,
! [X2: nat > nat] :
( ? [X4: nat,X5: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,X4)),vAPP(nat,nat,X2,X5)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) ) )
=> ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,vAPP(sTfun(nat,nat),nat,sK116,X2))),vAPP(nat,nat,X2,vAPP(sTfun(nat,nat),nat,sK117,X2))) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,nat),nat,sK116,X2)),vAPP(sTfun(nat,nat),nat,sK117,X2)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1370,plain,
! [X0: nat,X1: nat,X2: nat > nat,X3: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,X0)),X3) )
| ? [X4: nat,X5: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,X4)),vAPP(nat,nat,X2,X5)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,X1)),X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(flattening,[],[f1369]) ).
thf(f1369,plain,
! [X0: nat,X1: nat,X2: nat > nat,X3: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,X0)),X3) )
| ? [X4: nat,X5: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,X4)),vAPP(nat,nat,X2,X5)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,X1)),X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(ennf_transformation,[],[f951]) ).
thf(f951,plain,
! [X0: nat,X1: nat,X2: nat > nat,X3: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,X1)),X3) )
=> ( ! [X4: nat,X5: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,X4)),vAPP(nat,nat,X2,X5)) ) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,X0)),X3) ) ) ) ),
inference(fool_elimination,[],[f950]) ).
thf(f950,plain,
! [X0: nat,X1: nat,X2: nat > nat,X3: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,X1)),X3)
=> ( ! [X4: nat,X5: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,X4)),vAPP(nat,nat,X2,X5)) )
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,X0)),X3) ) ) ),
inference(rectify,[],[f101]) ).
thf(f101,axiom,
! [X13: nat,X12: nat,X25: nat > nat,X9: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X13),X12)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X25,X12)),X9)
=> ( ! [X4: nat,X26: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X26)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X25,X4)),vAPP(nat,nat,X25,X26)) )
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X25,X13)),X9) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_order__subst2) ).
thf(f6779,plain,
spl155_299,
inference(avatar_split_clause,[],[f2438,f6777]) ).
thf(f6777,plain,
( spl155_299
<=> ! [X0: nat,X3: set_nat,X2: nat > set_nat,X1: nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(nat,set_nat,X2,X0)),X3) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(nat,set_nat,X2,vAPP(sTfun(nat,set_nat),nat,sK114,X2))),vAPP(nat,set_nat,X2,vAPP(sTfun(nat,set_nat),nat,sK115,X2))) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(nat,set_nat,X2,X1)),X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_299])]) ).
thf(f2438,plain,
! [X2: nat > set_nat,X3: set_nat,X0: nat,X1: nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(nat,set_nat,X2,X0)),X3) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(nat,set_nat,X2,vAPP(sTfun(nat,set_nat),nat,sK114,X2))),vAPP(nat,set_nat,X2,vAPP(sTfun(nat,set_nat),nat,sK115,X2))) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(nat,set_nat,X2,X1)),X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),X1) ) ),
inference(definition_unfolding,[],[f2035,f1650,f1650,f1650,f1646]) ).
thf(f2035,plain,
! [X2: nat > set_nat,X3: set_nat,X0: nat,X1: nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(nat,set_nat,X2,X0)),X3) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(nat,set_nat,X2,vAPP(sTfun(nat,set_nat),nat,sK114,X2))),vAPP(nat,set_nat,X2,vAPP(sTfun(nat,set_nat),nat,sK115,X2))) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(nat,set_nat,X2,X1)),X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1574]) ).
thf(f1574,plain,
! [X0: nat,X1: nat,X2: nat > set_nat,X3: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(nat,set_nat,X2,X0)),X3) )
| ( ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(nat,set_nat,X2,vAPP(sTfun(nat,set_nat),nat,sK114,X2))),vAPP(nat,set_nat,X2,vAPP(sTfun(nat,set_nat),nat,sK115,X2))) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,set_nat),nat,sK114,X2)),vAPP(sTfun(nat,set_nat),nat,sK115,X2)) ) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(nat,set_nat,X2,X1)),X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK114,sK115])],[f1368,f1573]) ).
thf(f1573,plain,
! [X2: nat > set_nat] :
( ? [X4: nat,X5: nat] :
( ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(nat,set_nat,X2,X4)),vAPP(nat,set_nat,X2,X5)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) ) )
=> ( ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(nat,set_nat,X2,vAPP(sTfun(nat,set_nat),nat,sK114,X2))),vAPP(nat,set_nat,X2,vAPP(sTfun(nat,set_nat),nat,sK115,X2))) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,set_nat),nat,sK114,X2)),vAPP(sTfun(nat,set_nat),nat,sK115,X2)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1368,plain,
! [X0: nat,X1: nat,X2: nat > set_nat,X3: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(nat,set_nat,X2,X0)),X3) )
| ? [X4: nat,X5: nat] :
( ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(nat,set_nat,X2,X4)),vAPP(nat,set_nat,X2,X5)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) ) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(nat,set_nat,X2,X1)),X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(flattening,[],[f1367]) ).
thf(f1367,plain,
! [X0: nat,X1: nat,X2: nat > set_nat,X3: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(nat,set_nat,X2,X0)),X3) )
| ? [X4: nat,X5: nat] :
( ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(nat,set_nat,X2,X4)),vAPP(nat,set_nat,X2,X5)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) ) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(nat,set_nat,X2,X1)),X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(ennf_transformation,[],[f949]) ).
thf(f949,plain,
! [X0: nat,X1: nat,X2: nat > set_nat,X3: set_nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
=> ( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(nat,set_nat,X2,X1)),X3) )
=> ( ! [X4: nat,X5: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) )
=> ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(nat,set_nat,X2,X4)),vAPP(nat,set_nat,X2,X5)) ) )
=> ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(nat,set_nat,X2,X0)),X3) ) ) ) ),
inference(fool_elimination,[],[f948]) ).
thf(f948,plain,
! [X0: nat,X1: nat,X2: nat > set_nat,X3: set_nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1)
=> ( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(nat,set_nat,X2,X1)),X3)
=> ( ! [X4: nat,X5: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5)
=> vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(nat,set_nat,X2,X4)),vAPP(nat,set_nat,X2,X5)) )
=> vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(nat,set_nat,X2,X0)),X3) ) ) ),
inference(rectify,[],[f100]) ).
thf(f100,axiom,
! [X13: nat,X12: nat,X25: nat > set_nat,X9: set_nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X13),X12)
=> ( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(nat,set_nat,X25,X12)),X9)
=> ( ! [X4: nat,X26: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X26)
=> vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(nat,set_nat,X25,X4)),vAPP(nat,set_nat,X25,X26)) )
=> vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(nat,set_nat,X25,X13)),X9) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_order__subst2) ).
thf(f6775,plain,
spl155_298,
inference(avatar_split_clause,[],[f2429,f6773]) ).
thf(f6773,plain,
( spl155_298
<=> ! [X0: set_nat,X3: set_Pr1986765409at_nat,X2: set_nat > set_Pr1986765409at_nat,X1: set_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_nat,set_Pr1986765409at_nat,X2,X0)),X3) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_nat,set_Pr1986765409at_nat,X2,vAPP(sTfun(set_nat,set_Pr1986765409at_nat),set_nat,sK106,X2))),vAPP(set_nat,set_Pr1986765409at_nat,X2,vAPP(sTfun(set_nat,set_Pr1986765409at_nat),set_nat,sK107,X2))) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_nat,set_Pr1986765409at_nat,X2,X1)),X3) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_298])]) ).
thf(f2429,plain,
! [X2: set_nat > set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat,X0: set_nat,X1: set_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_nat,set_Pr1986765409at_nat,X2,X0)),X3) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_nat,set_Pr1986765409at_nat,X2,vAPP(sTfun(set_nat,set_Pr1986765409at_nat),set_nat,sK106,X2))),vAPP(set_nat,set_Pr1986765409at_nat,X2,vAPP(sTfun(set_nat,set_Pr1986765409at_nat),set_nat,sK107,X2))) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_nat,set_Pr1986765409at_nat,X2,X1)),X3) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),X1) ) ),
inference(definition_unfolding,[],[f2026,f1656,f1656,f1656,f1650]) ).
thf(f2026,plain,
! [X2: set_nat > set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat,X0: set_nat,X1: set_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_nat,set_Pr1986765409at_nat,X2,X0)),X3) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_nat,set_Pr1986765409at_nat,X2,vAPP(sTfun(set_nat,set_Pr1986765409at_nat),set_nat,sK106,X2))),vAPP(set_nat,set_Pr1986765409at_nat,X2,vAPP(sTfun(set_nat,set_Pr1986765409at_nat),set_nat,sK107,X2))) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_nat,set_Pr1986765409at_nat,X2,X1)),X3) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1566]) ).
thf(f1566,plain,
! [X0: set_nat,X1: set_nat,X2: set_nat > set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_nat,set_Pr1986765409at_nat,X2,X0)),X3) )
| ( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_nat,set_Pr1986765409at_nat,X2,vAPP(sTfun(set_nat,set_Pr1986765409at_nat),set_nat,sK106,X2))),vAPP(set_nat,set_Pr1986765409at_nat,X2,vAPP(sTfun(set_nat,set_Pr1986765409at_nat),set_nat,sK107,X2))) )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(sTfun(set_nat,set_Pr1986765409at_nat),set_nat,sK106,X2)),vAPP(sTfun(set_nat,set_Pr1986765409at_nat),set_nat,sK107,X2)) ) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_nat,set_Pr1986765409at_nat,X2,X1)),X3) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK106,sK107])],[f1358,f1565]) ).
thf(f1565,plain,
! [X2: set_nat > set_Pr1986765409at_nat] :
( ? [X4: set_nat,X5: set_nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_nat,set_Pr1986765409at_nat,X2,X4)),vAPP(set_nat,set_Pr1986765409at_nat,X2,X5)) )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X4),X5) ) )
=> ( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_nat,set_Pr1986765409at_nat,X2,vAPP(sTfun(set_nat,set_Pr1986765409at_nat),set_nat,sK106,X2))),vAPP(set_nat,set_Pr1986765409at_nat,X2,vAPP(sTfun(set_nat,set_Pr1986765409at_nat),set_nat,sK107,X2))) )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(sTfun(set_nat,set_Pr1986765409at_nat),set_nat,sK106,X2)),vAPP(sTfun(set_nat,set_Pr1986765409at_nat),set_nat,sK107,X2)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1358,plain,
! [X0: set_nat,X1: set_nat,X2: set_nat > set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_nat,set_Pr1986765409at_nat,X2,X0)),X3) )
| ? [X4: set_nat,X5: set_nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_nat,set_Pr1986765409at_nat,X2,X4)),vAPP(set_nat,set_Pr1986765409at_nat,X2,X5)) )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X4),X5) ) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_nat,set_Pr1986765409at_nat,X2,X1)),X3) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1) ) ),
inference(flattening,[],[f1357]) ).
thf(f1357,plain,
! [X0: set_nat,X1: set_nat,X2: set_nat > set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_nat,set_Pr1986765409at_nat,X2,X0)),X3) )
| ? [X4: set_nat,X5: set_nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_nat,set_Pr1986765409at_nat,X2,X4)),vAPP(set_nat,set_Pr1986765409at_nat,X2,X5)) )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X4),X5) ) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_nat,set_Pr1986765409at_nat,X2,X1)),X3) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1) ) ),
inference(ennf_transformation,[],[f939]) ).
thf(f939,plain,
! [X0: set_nat,X1: set_nat,X2: set_nat > set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1) )
=> ( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_nat,set_Pr1986765409at_nat,X2,X1)),X3) )
=> ( ! [X4: set_nat,X5: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X4),X5) )
=> ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_nat,set_Pr1986765409at_nat,X2,X4)),vAPP(set_nat,set_Pr1986765409at_nat,X2,X5)) ) )
=> ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_nat,set_Pr1986765409at_nat,X2,X0)),X3) ) ) ) ),
inference(fool_elimination,[],[f938]) ).
thf(f938,plain,
! [X0: set_nat,X1: set_nat,X2: set_nat > set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat] :
( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1)
=> ( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_nat,set_Pr1986765409at_nat,X2,X1)),X3)
=> ( ! [X4: set_nat,X5: set_nat] :
( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X4),X5)
=> vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_nat,set_Pr1986765409at_nat,X2,X4)),vAPP(set_nat,set_Pr1986765409at_nat,X2,X5)) )
=> vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_nat,set_Pr1986765409at_nat,X2,X0)),X3) ) ) ),
inference(rectify,[],[f96]) ).
thf(f96,axiom,
! [X13: set_nat,X12: set_nat,X25: set_nat > set_Pr1986765409at_nat,X9: set_Pr1986765409at_nat] :
( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X13),X12)
=> ( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_nat,set_Pr1986765409at_nat,X25,X12)),X9)
=> ( ! [X4: set_nat,X26: set_nat] :
( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X4),X26)
=> vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_nat,set_Pr1986765409at_nat,X25,X4)),vAPP(set_nat,set_Pr1986765409at_nat,X25,X26)) )
=> vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_nat,set_Pr1986765409at_nat,X25,X13)),X9) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_order__subst2) ).
thf(f6765,plain,
spl155_297,
inference(avatar_split_clause,[],[f2427,f6763]) ).
thf(f6763,plain,
( spl155_297
<=> ! [X0: set_nat,X3: nat,X2: set_nat > nat,X1: set_nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_nat,nat,X2,X0)),X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_nat,nat,X2,vAPP(sTfun(set_nat,nat),set_nat,sK104,X2))),vAPP(set_nat,nat,X2,vAPP(sTfun(set_nat,nat),set_nat,sK105,X2))) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_nat,nat,X2,X1)),X3) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_297])]) ).
thf(f2427,plain,
! [X2: set_nat > nat,X3: nat,X0: set_nat,X1: set_nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_nat,nat,X2,X0)),X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_nat,nat,X2,vAPP(sTfun(set_nat,nat),set_nat,sK104,X2))),vAPP(set_nat,nat,X2,vAPP(sTfun(set_nat,nat),set_nat,sK105,X2))) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_nat,nat,X2,X1)),X3) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),X1) ) ),
inference(definition_unfolding,[],[f2024,f1646,f1646,f1646,f1650]) ).
thf(f2024,plain,
! [X2: set_nat > nat,X3: nat,X0: set_nat,X1: set_nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,X2,X0)),X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,X2,vAPP(sTfun(set_nat,nat),set_nat,sK104,X2))),vAPP(set_nat,nat,X2,vAPP(sTfun(set_nat,nat),set_nat,sK105,X2))) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,X2,X1)),X3) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1564]) ).
thf(f1564,plain,
! [X0: set_nat,X1: set_nat,X2: set_nat > nat,X3: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,X2,X0)),X3) )
| ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,X2,vAPP(sTfun(set_nat,nat),set_nat,sK104,X2))),vAPP(set_nat,nat,X2,vAPP(sTfun(set_nat,nat),set_nat,sK105,X2))) )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(sTfun(set_nat,nat),set_nat,sK104,X2)),vAPP(sTfun(set_nat,nat),set_nat,sK105,X2)) ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,X2,X1)),X3) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK104,sK105])],[f1356,f1563]) ).
thf(f1563,plain,
! [X2: set_nat > nat] :
( ? [X4: set_nat,X5: set_nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,X2,X4)),vAPP(set_nat,nat,X2,X5)) )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X4),X5) ) )
=> ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,X2,vAPP(sTfun(set_nat,nat),set_nat,sK104,X2))),vAPP(set_nat,nat,X2,vAPP(sTfun(set_nat,nat),set_nat,sK105,X2))) )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(sTfun(set_nat,nat),set_nat,sK104,X2)),vAPP(sTfun(set_nat,nat),set_nat,sK105,X2)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1356,plain,
! [X0: set_nat,X1: set_nat,X2: set_nat > nat,X3: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,X2,X0)),X3) )
| ? [X4: set_nat,X5: set_nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,X2,X4)),vAPP(set_nat,nat,X2,X5)) )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X4),X5) ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,X2,X1)),X3) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1) ) ),
inference(flattening,[],[f1355]) ).
thf(f1355,plain,
! [X0: set_nat,X1: set_nat,X2: set_nat > nat,X3: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,X2,X0)),X3) )
| ? [X4: set_nat,X5: set_nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,X2,X4)),vAPP(set_nat,nat,X2,X5)) )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X4),X5) ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,X2,X1)),X3) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1) ) ),
inference(ennf_transformation,[],[f937]) ).
thf(f937,plain,
! [X0: set_nat,X1: set_nat,X2: set_nat > nat,X3: nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,X2,X1)),X3) )
=> ( ! [X4: set_nat,X5: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X4),X5) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,X2,X4)),vAPP(set_nat,nat,X2,X5)) ) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,X2,X0)),X3) ) ) ) ),
inference(fool_elimination,[],[f936]) ).
thf(f936,plain,
! [X0: set_nat,X1: set_nat,X2: set_nat > nat,X3: nat] :
( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,X2,X1)),X3)
=> ( ! [X4: set_nat,X5: set_nat] :
( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X4),X5)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,X2,X4)),vAPP(set_nat,nat,X2,X5)) )
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,X2,X0)),X3) ) ) ),
inference(rectify,[],[f98]) ).
thf(f98,axiom,
! [X13: set_nat,X12: set_nat,X25: set_nat > nat,X9: nat] :
( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X13),X12)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,X25,X12)),X9)
=> ( ! [X4: set_nat,X26: set_nat] :
( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X4),X26)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,X25,X4)),vAPP(set_nat,nat,X25,X26)) )
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,X25,X13)),X9) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_order__subst2) ).
thf(f6761,plain,
spl155_296,
inference(avatar_split_clause,[],[f2425,f6759]) ).
thf(f6759,plain,
( spl155_296
<=> ! [X0: set_nat,X3: set_nat,X2: set_nat > set_nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_nat,set_nat,X2,X0)),X3) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_nat,set_nat,X2,vAPP(sTfun(set_nat,set_nat),set_nat,sK102,X2))),vAPP(set_nat,set_nat,X2,vAPP(sTfun(set_nat,set_nat),set_nat,sK103,X2))) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_nat,set_nat,X2,X1)),X3) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_296])]) ).
thf(f2425,plain,
! [X2: set_nat > set_nat,X3: set_nat,X0: set_nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_nat,set_nat,X2,X0)),X3) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_nat,set_nat,X2,vAPP(sTfun(set_nat,set_nat),set_nat,sK102,X2))),vAPP(set_nat,set_nat,X2,vAPP(sTfun(set_nat,set_nat),set_nat,sK103,X2))) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_nat,set_nat,X2,X1)),X3) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),X1) ) ),
inference(definition_unfolding,[],[f2022,f1650,f1650,f1650,f1650]) ).
thf(f2022,plain,
! [X2: set_nat > set_nat,X3: set_nat,X0: set_nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,X2,X0)),X3) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,X2,vAPP(sTfun(set_nat,set_nat),set_nat,sK102,X2))),vAPP(set_nat,set_nat,X2,vAPP(sTfun(set_nat,set_nat),set_nat,sK103,X2))) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,X2,X1)),X3) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1562]) ).
thf(f1562,plain,
! [X0: set_nat,X1: set_nat,X2: set_nat > set_nat,X3: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,X2,X0)),X3) )
| ( ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,X2,vAPP(sTfun(set_nat,set_nat),set_nat,sK102,X2))),vAPP(set_nat,set_nat,X2,vAPP(sTfun(set_nat,set_nat),set_nat,sK103,X2))) )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(sTfun(set_nat,set_nat),set_nat,sK102,X2)),vAPP(sTfun(set_nat,set_nat),set_nat,sK103,X2)) ) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,X2,X1)),X3) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK102,sK103])],[f1354,f1561]) ).
thf(f1561,plain,
! [X2: set_nat > set_nat] :
( ? [X4: set_nat,X5: set_nat] :
( ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,X2,X4)),vAPP(set_nat,set_nat,X2,X5)) )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X4),X5) ) )
=> ( ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,X2,vAPP(sTfun(set_nat,set_nat),set_nat,sK102,X2))),vAPP(set_nat,set_nat,X2,vAPP(sTfun(set_nat,set_nat),set_nat,sK103,X2))) )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(sTfun(set_nat,set_nat),set_nat,sK102,X2)),vAPP(sTfun(set_nat,set_nat),set_nat,sK103,X2)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1354,plain,
! [X0: set_nat,X1: set_nat,X2: set_nat > set_nat,X3: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,X2,X0)),X3) )
| ? [X4: set_nat,X5: set_nat] :
( ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,X2,X4)),vAPP(set_nat,set_nat,X2,X5)) )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X4),X5) ) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,X2,X1)),X3) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1) ) ),
inference(flattening,[],[f1353]) ).
thf(f1353,plain,
! [X0: set_nat,X1: set_nat,X2: set_nat > set_nat,X3: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,X2,X0)),X3) )
| ? [X4: set_nat,X5: set_nat] :
( ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,X2,X4)),vAPP(set_nat,set_nat,X2,X5)) )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X4),X5) ) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,X2,X1)),X3) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1) ) ),
inference(ennf_transformation,[],[f935]) ).
thf(f935,plain,
! [X0: set_nat,X1: set_nat,X2: set_nat > set_nat,X3: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1) )
=> ( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,X2,X1)),X3) )
=> ( ! [X4: set_nat,X5: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X4),X5) )
=> ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,X2,X4)),vAPP(set_nat,set_nat,X2,X5)) ) )
=> ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,X2,X0)),X3) ) ) ) ),
inference(fool_elimination,[],[f934]) ).
thf(f934,plain,
! [X0: set_nat,X1: set_nat,X2: set_nat > set_nat,X3: set_nat] :
( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1)
=> ( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,X2,X1)),X3)
=> ( ! [X4: set_nat,X5: set_nat] :
( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X4),X5)
=> vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,X2,X4)),vAPP(set_nat,set_nat,X2,X5)) )
=> vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,X2,X0)),X3) ) ) ),
inference(rectify,[],[f97]) ).
thf(f97,axiom,
! [X13: set_nat,X12: set_nat,X25: set_nat > set_nat,X9: set_nat] :
( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X13),X12)
=> ( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,X25,X12)),X9)
=> ( ! [X4: set_nat,X26: set_nat] :
( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X4),X26)
=> vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,X25,X4)),vAPP(set_nat,set_nat,X25,X26)) )
=> vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,X25,X13)),X9) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_order__subst2) ).
thf(f6505,plain,
spl155_295,
inference(avatar_split_clause,[],[f2478,f6503]) ).
thf(f6503,plain,
( spl155_295
<=> ! [X0: set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat > set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X1,X3)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),set_Pr1986765409at_nat,sK149,X1)),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),set_Pr1986765409at_nat,sK150,X1)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X2),X3) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X1,X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_295])]) ).
thf(f2478,plain,
! [X2: set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat > set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X1,X3)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),set_Pr1986765409at_nat,sK149,X1)),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),set_Pr1986765409at_nat,sK150,X1)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X2),X3) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X1,X2)) ) ),
inference(definition_unfolding,[],[f2073,f1656,f1656,f1656,f1656]) ).
thf(f2073,plain,
! [X2: set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat > set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X1,X3)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),set_Pr1986765409at_nat,sK149,X1)),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),set_Pr1986765409at_nat,sK150,X1)) )
| ( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X2),X3) != $true )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X1,X2)) ) ),
inference(cnf_transformation,[],[f1610]) ).
thf(f6501,plain,
spl155_294,
inference(avatar_split_clause,[],[f2476,f6499]) ).
thf(f6499,plain,
( spl155_294
<=> ! [X0: set_Pr1986765409at_nat,X3: nat,X2: nat,X1: nat > set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),vAPP(nat,set_Pr1986765409at_nat,X1,X3)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(sTfun(nat,set_Pr1986765409at_nat),nat,sK147,X1)),vAPP(sTfun(nat,set_Pr1986765409at_nat),nat,sK148,X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X2),X3) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),vAPP(nat,set_Pr1986765409at_nat,X1,X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_294])]) ).
thf(f2476,plain,
! [X2: nat,X3: nat,X0: set_Pr1986765409at_nat,X1: nat > set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),vAPP(nat,set_Pr1986765409at_nat,X1,X3)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(sTfun(nat,set_Pr1986765409at_nat),nat,sK147,X1)),vAPP(sTfun(nat,set_Pr1986765409at_nat),nat,sK148,X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X2),X3) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),vAPP(nat,set_Pr1986765409at_nat,X1,X2)) ) ),
inference(definition_unfolding,[],[f2071,f1656,f1646,f1646,f1656]) ).
thf(f2071,plain,
! [X2: nat,X3: nat,X0: set_Pr1986765409at_nat,X1: nat > set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),vAPP(nat,set_Pr1986765409at_nat,X1,X3)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,set_Pr1986765409at_nat),nat,sK147,X1)),vAPP(sTfun(nat,set_Pr1986765409at_nat),nat,sK148,X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),vAPP(nat,set_Pr1986765409at_nat,X1,X2)) ) ),
inference(cnf_transformation,[],[f1608]) ).
thf(f6497,plain,
spl155_293,
inference(avatar_split_clause,[],[f2474,f6495]) ).
thf(f6495,plain,
( spl155_293
<=> ! [X0: set_Pr1986765409at_nat,X3: set_nat,X2: set_nat,X1: set_nat > set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),vAPP(set_nat,set_Pr1986765409at_nat,X1,X3)) )
| ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(sTfun(set_nat,set_Pr1986765409at_nat),set_nat,sK145,X1)),vAPP(sTfun(set_nat,set_Pr1986765409at_nat),set_nat,sK146,X1)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X2),X3) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),vAPP(set_nat,set_Pr1986765409at_nat,X1,X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_293])]) ).
thf(f2474,plain,
! [X2: set_nat,X3: set_nat,X0: set_Pr1986765409at_nat,X1: set_nat > set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),vAPP(set_nat,set_Pr1986765409at_nat,X1,X3)) )
| ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(sTfun(set_nat,set_Pr1986765409at_nat),set_nat,sK145,X1)),vAPP(sTfun(set_nat,set_Pr1986765409at_nat),set_nat,sK146,X1)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X2),X3) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),vAPP(set_nat,set_Pr1986765409at_nat,X1,X2)) ) ),
inference(definition_unfolding,[],[f2069,f1656,f1650,f1650,f1656]) ).
thf(f2069,plain,
! [X2: set_nat,X3: set_nat,X0: set_Pr1986765409at_nat,X1: set_nat > set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),vAPP(set_nat,set_Pr1986765409at_nat,X1,X3)) )
| ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(sTfun(set_nat,set_Pr1986765409at_nat),set_nat,sK145,X1)),vAPP(sTfun(set_nat,set_Pr1986765409at_nat),set_nat,sK146,X1)) )
| ( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X3) != $true )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),vAPP(set_nat,set_Pr1986765409at_nat,X1,X2)) ) ),
inference(cnf_transformation,[],[f1606]) ).
thf(f6493,plain,
spl155_292,
inference(avatar_split_clause,[],[f2472,f6491]) ).
thf(f6491,plain,
( spl155_292
<=> ! [X0: nat,X3: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat > nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),vAPP(set_Pr1986765409at_nat,nat,X1,X3)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(sTfun(set_Pr1986765409at_nat,nat),set_Pr1986765409at_nat,sK143,X1)),vAPP(sTfun(set_Pr1986765409at_nat,nat),set_Pr1986765409at_nat,sK144,X1)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X2),X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),vAPP(set_Pr1986765409at_nat,nat,X1,X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_292])]) ).
thf(f2472,plain,
! [X2: set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat,X0: nat,X1: set_Pr1986765409at_nat > nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),vAPP(set_Pr1986765409at_nat,nat,X1,X3)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(sTfun(set_Pr1986765409at_nat,nat),set_Pr1986765409at_nat,sK143,X1)),vAPP(sTfun(set_Pr1986765409at_nat,nat),set_Pr1986765409at_nat,sK144,X1)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X2),X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),vAPP(set_Pr1986765409at_nat,nat,X1,X2)) ) ),
inference(definition_unfolding,[],[f2067,f1646,f1656,f1656,f1646]) ).
thf(f2067,plain,
! [X2: set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat,X0: nat,X1: set_Pr1986765409at_nat > nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(set_Pr1986765409at_nat,nat,X1,X3)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(sTfun(set_Pr1986765409at_nat,nat),set_Pr1986765409at_nat,sK143,X1)),vAPP(sTfun(set_Pr1986765409at_nat,nat),set_Pr1986765409at_nat,sK144,X1)) )
| ( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X2),X3) != $true )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(set_Pr1986765409at_nat,nat,X1,X2)) ) ),
inference(cnf_transformation,[],[f1604]) ).
thf(f6489,plain,
spl155_291,
inference(avatar_split_clause,[],[f2470,f6487]) ).
thf(f6487,plain,
( spl155_291
<=> ! [X0: nat,X3: nat,X2: nat,X1: nat > nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),vAPP(nat,nat,X1,X3)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(sTfun(nat,nat),nat,sK141,X1)),vAPP(sTfun(nat,nat),nat,sK142,X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X2),X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),vAPP(nat,nat,X1,X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_291])]) ).
thf(f2470,plain,
! [X2: nat,X3: nat,X0: nat,X1: nat > nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),vAPP(nat,nat,X1,X3)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(sTfun(nat,nat),nat,sK141,X1)),vAPP(sTfun(nat,nat),nat,sK142,X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X2),X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),vAPP(nat,nat,X1,X2)) ) ),
inference(definition_unfolding,[],[f2065,f1646,f1646,f1646,f1646]) ).
thf(f2065,plain,
! [X2: nat,X3: nat,X0: nat,X1: nat > nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,X1,X3)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,nat),nat,sK141,X1)),vAPP(sTfun(nat,nat),nat,sK142,X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,X1,X2)) ) ),
inference(cnf_transformation,[],[f1602]) ).
thf(f6485,plain,
spl155_290,
inference(avatar_split_clause,[],[f2468,f6483]) ).
thf(f6483,plain,
( spl155_290
<=> ! [X0: nat,X3: set_nat,X2: set_nat,X1: set_nat > nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),vAPP(set_nat,nat,X1,X3)) )
| ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(sTfun(set_nat,nat),set_nat,sK139,X1)),vAPP(sTfun(set_nat,nat),set_nat,sK140,X1)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X2),X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),vAPP(set_nat,nat,X1,X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_290])]) ).
thf(f2468,plain,
! [X2: set_nat,X3: set_nat,X0: nat,X1: set_nat > nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),vAPP(set_nat,nat,X1,X3)) )
| ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(sTfun(set_nat,nat),set_nat,sK139,X1)),vAPP(sTfun(set_nat,nat),set_nat,sK140,X1)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X2),X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),vAPP(set_nat,nat,X1,X2)) ) ),
inference(definition_unfolding,[],[f2063,f1646,f1650,f1650,f1646]) ).
thf(f2063,plain,
! [X2: set_nat,X3: set_nat,X0: nat,X1: set_nat > nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(set_nat,nat,X1,X3)) )
| ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(sTfun(set_nat,nat),set_nat,sK139,X1)),vAPP(sTfun(set_nat,nat),set_nat,sK140,X1)) )
| ( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X3) != $true )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(set_nat,nat,X1,X2)) ) ),
inference(cnf_transformation,[],[f1600]) ).
thf(f6481,plain,
spl155_289,
inference(avatar_split_clause,[],[f2466,f6479]) ).
thf(f6479,plain,
( spl155_289
<=> ! [X0: set_nat,X3: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat > set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),vAPP(set_Pr1986765409at_nat,set_nat,X1,X3)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(sTfun(set_Pr1986765409at_nat,set_nat),set_Pr1986765409at_nat,sK137,X1)),vAPP(sTfun(set_Pr1986765409at_nat,set_nat),set_Pr1986765409at_nat,sK138,X1)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X2),X3) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),vAPP(set_Pr1986765409at_nat,set_nat,X1,X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_289])]) ).
thf(f2466,plain,
! [X2: set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat,X0: set_nat,X1: set_Pr1986765409at_nat > set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),vAPP(set_Pr1986765409at_nat,set_nat,X1,X3)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(sTfun(set_Pr1986765409at_nat,set_nat),set_Pr1986765409at_nat,sK137,X1)),vAPP(sTfun(set_Pr1986765409at_nat,set_nat),set_Pr1986765409at_nat,sK138,X1)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X2),X3) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),vAPP(set_Pr1986765409at_nat,set_nat,X1,X2)) ) ),
inference(definition_unfolding,[],[f2061,f1650,f1656,f1656,f1650]) ).
thf(f2061,plain,
! [X2: set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat,X0: set_nat,X1: set_Pr1986765409at_nat > set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),vAPP(set_Pr1986765409at_nat,set_nat,X1,X3)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(sTfun(set_Pr1986765409at_nat,set_nat),set_Pr1986765409at_nat,sK137,X1)),vAPP(sTfun(set_Pr1986765409at_nat,set_nat),set_Pr1986765409at_nat,sK138,X1)) )
| ( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X2),X3) != $true )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),vAPP(set_Pr1986765409at_nat,set_nat,X1,X2)) ) ),
inference(cnf_transformation,[],[f1598]) ).
thf(f6477,plain,
spl155_288,
inference(avatar_split_clause,[],[f2464,f6475]) ).
thf(f6475,plain,
( spl155_288
<=> ! [X0: set_nat,X3: nat,X2: nat,X1: nat > set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),vAPP(nat,set_nat,X1,X3)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(sTfun(nat,set_nat),nat,sK135,X1)),vAPP(sTfun(nat,set_nat),nat,sK136,X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X2),X3) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),vAPP(nat,set_nat,X1,X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_288])]) ).
thf(f2464,plain,
! [X2: nat,X3: nat,X0: set_nat,X1: nat > set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),vAPP(nat,set_nat,X1,X3)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(sTfun(nat,set_nat),nat,sK135,X1)),vAPP(sTfun(nat,set_nat),nat,sK136,X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X2),X3) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),vAPP(nat,set_nat,X1,X2)) ) ),
inference(definition_unfolding,[],[f2059,f1650,f1646,f1646,f1650]) ).
thf(f2059,plain,
! [X2: nat,X3: nat,X0: set_nat,X1: nat > set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),vAPP(nat,set_nat,X1,X3)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,set_nat),nat,sK135,X1)),vAPP(sTfun(nat,set_nat),nat,sK136,X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),vAPP(nat,set_nat,X1,X2)) ) ),
inference(cnf_transformation,[],[f1596]) ).
thf(f6473,plain,
spl155_287,
inference(avatar_split_clause,[],[f2462,f6471]) ).
thf(f6471,plain,
( spl155_287
<=> ! [X0: set_nat,X3: set_nat,X2: set_nat,X1: set_nat > set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),vAPP(set_nat,set_nat,X1,X3)) )
| ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(sTfun(set_nat,set_nat),set_nat,sK133,X1)),vAPP(sTfun(set_nat,set_nat),set_nat,sK134,X1)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X2),X3) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),vAPP(set_nat,set_nat,X1,X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_287])]) ).
thf(f2462,plain,
! [X2: set_nat,X3: set_nat,X0: set_nat,X1: set_nat > set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),vAPP(set_nat,set_nat,X1,X3)) )
| ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(sTfun(set_nat,set_nat),set_nat,sK133,X1)),vAPP(sTfun(set_nat,set_nat),set_nat,sK134,X1)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X2),X3) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),vAPP(set_nat,set_nat,X1,X2)) ) ),
inference(definition_unfolding,[],[f2057,f1650,f1650,f1650,f1650]) ).
thf(f2057,plain,
! [X2: set_nat,X3: set_nat,X0: set_nat,X1: set_nat > set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),vAPP(set_nat,set_nat,X1,X3)) )
| ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(sTfun(set_nat,set_nat),set_nat,sK133,X1)),vAPP(sTfun(set_nat,set_nat),set_nat,sK134,X1)) )
| ( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X3) != $true )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),vAPP(set_nat,set_nat,X1,X2)) ) ),
inference(cnf_transformation,[],[f1594]) ).
thf(f6469,plain,
spl155_286,
inference(avatar_split_clause,[],[f2460,f6467]) ).
thf(f6467,plain,
( spl155_286
<=> ! [X0: set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat > set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X2,X0)),X3) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),set_Pr1986765409at_nat,sK131,X2)),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),set_Pr1986765409at_nat,sK132,X2)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X2,X1)),X3) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_286])]) ).
thf(f2460,plain,
! [X2: set_Pr1986765409at_nat > set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X2,X0)),X3) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),set_Pr1986765409at_nat,sK131,X2)),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),set_Pr1986765409at_nat,sK132,X2)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X2,X1)),X3) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X1) ) ),
inference(definition_unfolding,[],[f2055,f1656,f1656,f1656,f1656]) ).
thf(f2055,plain,
! [X2: set_Pr1986765409at_nat > set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X2,X0)),X3) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),set_Pr1986765409at_nat,sK131,X2)),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),set_Pr1986765409at_nat,sK132,X2)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X2,X1)),X3) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1592]) ).
thf(f6465,plain,
( spl155_285
| ~ spl155_245
| ~ spl155_257 ),
inference(avatar_split_clause,[],[f6251,f6217,f6127,f6463]) ).
thf(f6463,plain,
( spl155_285
<=> ! [X0: nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),outgoing_a,c),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_285])]) ).
thf(f6251,plain,
( ! [X0: nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),outgoing_a,c),X0)) )
| ~ spl155_245
| ~ spl155_257 ),
inference(trivial_inequality_removal,[],[f6244]) ).
thf(f6244,plain,
( ! [X0: nat] :
( ( $true != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),outgoing_a,c),X0)) ) )
| ~ spl155_245
| ~ spl155_257 ),
inference(superposition,[],[f6218,f6129]) ).
thf(f6461,plain,
spl155_284,
inference(avatar_split_clause,[],[f2458,f6459]) ).
thf(f6459,plain,
( spl155_284
<=> ! [X0: set_Pr1986765409at_nat,X3: nat,X2: set_Pr1986765409at_nat > nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,nat,X2,X0)),X3) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(sTfun(set_Pr1986765409at_nat,nat),set_Pr1986765409at_nat,sK129,X2)),vAPP(sTfun(set_Pr1986765409at_nat,nat),set_Pr1986765409at_nat,sK130,X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,nat,X2,X1)),X3) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_284])]) ).
thf(f2458,plain,
! [X2: set_Pr1986765409at_nat > nat,X3: nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,nat,X2,X0)),X3) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(sTfun(set_Pr1986765409at_nat,nat),set_Pr1986765409at_nat,sK129,X2)),vAPP(sTfun(set_Pr1986765409at_nat,nat),set_Pr1986765409at_nat,sK130,X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,nat,X2,X1)),X3) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X1) ) ),
inference(definition_unfolding,[],[f2053,f1646,f1656,f1646,f1656]) ).
thf(f2053,plain,
! [X2: set_Pr1986765409at_nat > nat,X3: nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,X2,X0)),X3) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(sTfun(set_Pr1986765409at_nat,nat),set_Pr1986765409at_nat,sK129,X2)),vAPP(sTfun(set_Pr1986765409at_nat,nat),set_Pr1986765409at_nat,sK130,X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,X2,X1)),X3) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1590]) ).
thf(f6457,plain,
spl155_283,
inference(avatar_split_clause,[],[f2456,f6455]) ).
thf(f6455,plain,
( spl155_283
<=> ! [X0: set_Pr1986765409at_nat,X3: set_nat,X2: set_Pr1986765409at_nat > set_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_nat,X2,X0)),X3) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(sTfun(set_Pr1986765409at_nat,set_nat),set_Pr1986765409at_nat,sK127,X2)),vAPP(sTfun(set_Pr1986765409at_nat,set_nat),set_Pr1986765409at_nat,sK128,X2)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_nat,X2,X1)),X3) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_283])]) ).
thf(f2456,plain,
! [X2: set_Pr1986765409at_nat > set_nat,X3: set_nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_nat,X2,X0)),X3) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(sTfun(set_Pr1986765409at_nat,set_nat),set_Pr1986765409at_nat,sK127,X2)),vAPP(sTfun(set_Pr1986765409at_nat,set_nat),set_Pr1986765409at_nat,sK128,X2)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_nat,X2,X1)),X3) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X1) ) ),
inference(definition_unfolding,[],[f2051,f1650,f1656,f1650,f1656]) ).
thf(f2051,plain,
! [X2: set_Pr1986765409at_nat > set_nat,X3: set_nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_Pr1986765409at_nat,set_nat,X2,X0)),X3) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(sTfun(set_Pr1986765409at_nat,set_nat),set_Pr1986765409at_nat,sK127,X2)),vAPP(sTfun(set_Pr1986765409at_nat,set_nat),set_Pr1986765409at_nat,sK128,X2)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_Pr1986765409at_nat,set_nat,X2,X1)),X3) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1588]) ).
thf(f6453,plain,
spl155_282,
inference(avatar_split_clause,[],[f2443,f6451]) ).
thf(f6451,plain,
( spl155_282
<=> ! [X0: nat,X3: set_Pr1986765409at_nat,X2: nat > set_Pr1986765409at_nat,X1: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(nat,set_Pr1986765409at_nat,X2,X0)),X3) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(sTfun(nat,set_Pr1986765409at_nat),nat,sK118,X2)),vAPP(sTfun(nat,set_Pr1986765409at_nat),nat,sK119,X2)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(nat,set_Pr1986765409at_nat,X2,X1)),X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_282])]) ).
thf(f2443,plain,
! [X2: nat > set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat,X0: nat,X1: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(nat,set_Pr1986765409at_nat,X2,X0)),X3) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(sTfun(nat,set_Pr1986765409at_nat),nat,sK118,X2)),vAPP(sTfun(nat,set_Pr1986765409at_nat),nat,sK119,X2)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(nat,set_Pr1986765409at_nat,X2,X1)),X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),X1) ) ),
inference(definition_unfolding,[],[f2038,f1656,f1646,f1656,f1646]) ).
thf(f2038,plain,
! [X2: nat > set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat,X0: nat,X1: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(nat,set_Pr1986765409at_nat,X2,X0)),X3) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,set_Pr1986765409at_nat),nat,sK118,X2)),vAPP(sTfun(nat,set_Pr1986765409at_nat),nat,sK119,X2)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(nat,set_Pr1986765409at_nat,X2,X1)),X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1578]) ).
thf(f6449,plain,
spl155_281,
inference(avatar_split_clause,[],[f2441,f6447]) ).
thf(f6447,plain,
( spl155_281
<=> ! [X0: nat,X3: nat,X2: nat > nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(nat,nat,X2,X0)),X3) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(sTfun(nat,nat),nat,sK116,X2)),vAPP(sTfun(nat,nat),nat,sK117,X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(nat,nat,X2,X1)),X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_281])]) ).
thf(f2441,plain,
! [X2: nat > nat,X3: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(nat,nat,X2,X0)),X3) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(sTfun(nat,nat),nat,sK116,X2)),vAPP(sTfun(nat,nat),nat,sK117,X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(nat,nat,X2,X1)),X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),X1) ) ),
inference(definition_unfolding,[],[f2036,f1646,f1646,f1646,f1646]) ).
thf(f2036,plain,
! [X2: nat > nat,X3: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,X0)),X3) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,nat),nat,sK116,X2)),vAPP(sTfun(nat,nat),nat,sK117,X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,X1)),X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1576]) ).
thf(f6445,plain,
spl155_280,
inference(avatar_split_clause,[],[f2439,f6443]) ).
thf(f6443,plain,
( spl155_280
<=> ! [X0: nat,X3: set_nat,X2: nat > set_nat,X1: nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(nat,set_nat,X2,X0)),X3) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(sTfun(nat,set_nat),nat,sK114,X2)),vAPP(sTfun(nat,set_nat),nat,sK115,X2)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(nat,set_nat,X2,X1)),X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_280])]) ).
thf(f2439,plain,
! [X2: nat > set_nat,X3: set_nat,X0: nat,X1: nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(nat,set_nat,X2,X0)),X3) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(sTfun(nat,set_nat),nat,sK114,X2)),vAPP(sTfun(nat,set_nat),nat,sK115,X2)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(nat,set_nat,X2,X1)),X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),X1) ) ),
inference(definition_unfolding,[],[f2034,f1650,f1646,f1650,f1646]) ).
thf(f2034,plain,
! [X2: nat > set_nat,X3: set_nat,X0: nat,X1: nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(nat,set_nat,X2,X0)),X3) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,set_nat),nat,sK114,X2)),vAPP(sTfun(nat,set_nat),nat,sK115,X2)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(nat,set_nat,X2,X1)),X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1574]) ).
thf(f6441,plain,
spl155_279,
inference(avatar_split_clause,[],[f2430,f6439]) ).
thf(f6439,plain,
( spl155_279
<=> ! [X0: set_nat,X3: set_Pr1986765409at_nat,X2: set_nat > set_Pr1986765409at_nat,X1: set_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_nat,set_Pr1986765409at_nat,X2,X0)),X3) )
| ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(sTfun(set_nat,set_Pr1986765409at_nat),set_nat,sK106,X2)),vAPP(sTfun(set_nat,set_Pr1986765409at_nat),set_nat,sK107,X2)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_nat,set_Pr1986765409at_nat,X2,X1)),X3) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_279])]) ).
thf(f2430,plain,
! [X2: set_nat > set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat,X0: set_nat,X1: set_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_nat,set_Pr1986765409at_nat,X2,X0)),X3) )
| ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(sTfun(set_nat,set_Pr1986765409at_nat),set_nat,sK106,X2)),vAPP(sTfun(set_nat,set_Pr1986765409at_nat),set_nat,sK107,X2)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_nat,set_Pr1986765409at_nat,X2,X1)),X3) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),X1) ) ),
inference(definition_unfolding,[],[f2025,f1656,f1650,f1656,f1650]) ).
thf(f2025,plain,
! [X2: set_nat > set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat,X0: set_nat,X1: set_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_nat,set_Pr1986765409at_nat,X2,X0)),X3) )
| ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(sTfun(set_nat,set_Pr1986765409at_nat),set_nat,sK106,X2)),vAPP(sTfun(set_nat,set_Pr1986765409at_nat),set_nat,sK107,X2)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_nat,set_Pr1986765409at_nat,X2,X1)),X3) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1566]) ).
thf(f6437,plain,
spl155_278,
inference(avatar_split_clause,[],[f2428,f6435]) ).
thf(f6435,plain,
( spl155_278
<=> ! [X0: set_nat,X3: nat,X2: set_nat > nat,X1: set_nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_nat,nat,X2,X0)),X3) )
| ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(sTfun(set_nat,nat),set_nat,sK104,X2)),vAPP(sTfun(set_nat,nat),set_nat,sK105,X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_nat,nat,X2,X1)),X3) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_278])]) ).
thf(f2428,plain,
! [X2: set_nat > nat,X3: nat,X0: set_nat,X1: set_nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_nat,nat,X2,X0)),X3) )
| ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(sTfun(set_nat,nat),set_nat,sK104,X2)),vAPP(sTfun(set_nat,nat),set_nat,sK105,X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_nat,nat,X2,X1)),X3) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),X1) ) ),
inference(definition_unfolding,[],[f2023,f1646,f1650,f1646,f1650]) ).
thf(f2023,plain,
! [X2: set_nat > nat,X3: nat,X0: set_nat,X1: set_nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,X2,X0)),X3) )
| ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(sTfun(set_nat,nat),set_nat,sK104,X2)),vAPP(sTfun(set_nat,nat),set_nat,sK105,X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,X2,X1)),X3) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1564]) ).
thf(f6433,plain,
spl155_277,
inference(avatar_split_clause,[],[f2426,f6431]) ).
thf(f6431,plain,
( spl155_277
<=> ! [X0: set_nat,X3: set_nat,X2: set_nat > set_nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_nat,set_nat,X2,X0)),X3) )
| ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(sTfun(set_nat,set_nat),set_nat,sK102,X2)),vAPP(sTfun(set_nat,set_nat),set_nat,sK103,X2)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_nat,set_nat,X2,X1)),X3) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_277])]) ).
thf(f2426,plain,
! [X2: set_nat > set_nat,X3: set_nat,X0: set_nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_nat,set_nat,X2,X0)),X3) )
| ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(sTfun(set_nat,set_nat),set_nat,sK102,X2)),vAPP(sTfun(set_nat,set_nat),set_nat,sK103,X2)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_nat,set_nat,X2,X1)),X3) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),X1) ) ),
inference(definition_unfolding,[],[f2021,f1650,f1650,f1650,f1650]) ).
thf(f2021,plain,
! [X2: set_nat > set_nat,X3: set_nat,X0: set_nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,X2,X0)),X3) )
| ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(sTfun(set_nat,set_nat),set_nat,sK102,X2)),vAPP(sTfun(set_nat,set_nat),set_nat,sK103,X2)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,X2,X1)),X3) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1562]) ).
thf(f6415,plain,
( spl155_276
| ~ spl155_245
| ~ spl155_256 ),
inference(avatar_split_clause,[],[f6243,f6213,f6127,f6413]) ).
thf(f6413,plain,
( spl155_276
<=> ! [X0: nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),incoming_a,c),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_276])]) ).
thf(f6243,plain,
( ! [X0: nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),incoming_a,c),X0)) )
| ~ spl155_245
| ~ spl155_256 ),
inference(trivial_inequality_removal,[],[f6236]) ).
thf(f6236,plain,
( ! [X0: nat] :
( ( $true != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),incoming_a,c),X0)) ) )
| ~ spl155_245
| ~ spl155_256 ),
inference(superposition,[],[f6214,f6129]) ).
thf(f6406,plain,
spl155_275,
inference(avatar_split_clause,[],[f2332,f6404]) ).
thf(f6404,plain,
( spl155_275
<=> ! [X2: set_Pr1986765409at_nat,X0: set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),X2) = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),X0,X1),X2) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK53,X0)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),X0,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK54,X0)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK55,X0))) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),X0,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK56,X0)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK57,X0))),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK57,X0)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),X0,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK58,X0)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK59,X0))),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK58,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_275])]) ).
thf(f2332,plain,
! [X2: set_Pr1986765409at_nat,X0: set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),X2) = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),X0,X1),X2) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK53,X0)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),X0,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK54,X0)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK55,X0))) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),X0,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK56,X0)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK57,X0))),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK57,X0)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),X0,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK58,X0)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK59,X0))),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK58,X0)) ) ),
inference(definition_unfolding,[],[f1899,f1656,f1656,f1656]) ).
thf(f1899,plain,
! [X2: set_Pr1986765409at_nat,X0: set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),X2) = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),X0,X1),X2) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK53,X0)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),X0,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK54,X0)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK55,X0))) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),X0,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK56,X0)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK57,X0))),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK57,X0)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),X0,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK58,X0)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK59,X0))),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK58,X0)) ) ),
inference(cnf_transformation,[],[f1516]) ).
thf(f1516,plain,
! [X0: set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat] :
( ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),X2) = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),X0,X1),X2) )
| ( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK53,X0)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),X0,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK54,X0)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK55,X0))) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK53,X0)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK55,X0)) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK53,X0)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK54,X0)) ) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),X0,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK56,X0)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK57,X0))),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK57,X0)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),X0,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK58,X0)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK59,X0))),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK58,X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56,sK57,sK58,sK59])],[f1512,f1515,f1514,f1513]) ).
thf(f1513,plain,
! [X0: set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat] :
( ? [X3: set_Pr1986765409at_nat,X4: set_Pr1986765409at_nat,X5: set_Pr1986765409at_nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X3),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),X0,X4),X5)) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X3),X5) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X3),X4) ) )
=> ( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK53,X0)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),X0,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK54,X0)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK55,X0))) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK53,X0)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK55,X0)) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK53,X0)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK54,X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1514,plain,
! [X0: set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat] :
( ? [X6: set_Pr1986765409at_nat,X7: set_Pr1986765409at_nat] : ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),X0,X6),X7)),X7) )
=> ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),X0,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK56,X0)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK57,X0))),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK57,X0)) ) ),
introduced(choice_axiom,[]) ).
thf(f1515,plain,
! [X0: set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat] :
( ? [X8: set_Pr1986765409at_nat,X9: set_Pr1986765409at_nat] : ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),X0,X8),X9)),X8) )
=> ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),X0,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK58,X0)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK59,X0))),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK58,X0)) ) ),
introduced(choice_axiom,[]) ).
thf(f1512,plain,
! [X0: set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat] :
( ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),X2) = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),X0,X1),X2) )
| ? [X3: set_Pr1986765409at_nat,X4: set_Pr1986765409at_nat,X5: set_Pr1986765409at_nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X3),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),X0,X4),X5)) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X3),X5) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X3),X4) ) )
| ? [X6: set_Pr1986765409at_nat,X7: set_Pr1986765409at_nat] : ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),X0,X6),X7)),X7) )
| ? [X8: set_Pr1986765409at_nat,X9: set_Pr1986765409at_nat] : ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),X0,X8),X9)),X8) ) ),
inference(rectify,[],[f1217]) ).
thf(f1217,plain,
! [X0: set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat] :
( ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),X2) = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),X0,X1),X2) )
| ? [X7: set_Pr1986765409at_nat,X8: set_Pr1986765409at_nat,X9: set_Pr1986765409at_nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X7),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),X0,X8),X9)) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X7),X9) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X7),X8) ) )
| ? [X5: set_Pr1986765409at_nat,X6: set_Pr1986765409at_nat] : ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),X0,X5),X6)),X6) )
| ? [X3: set_Pr1986765409at_nat,X4: set_Pr1986765409at_nat] : ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),X0,X3),X4)),X3) ) ),
inference(flattening,[],[f1216]) ).
thf(f1216,plain,
! [X0: set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat] :
( ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),X2) = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),X0,X1),X2) )
| ? [X7: set_Pr1986765409at_nat,X8: set_Pr1986765409at_nat,X9: set_Pr1986765409at_nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X7),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),X0,X8),X9)) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X7),X9) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X7),X8) ) )
| ? [X5: set_Pr1986765409at_nat,X6: set_Pr1986765409at_nat] : ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),X0,X5),X6)),X6) )
| ? [X3: set_Pr1986765409at_nat,X4: set_Pr1986765409at_nat] : ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),X0,X3),X4)),X3) ) ),
inference(ennf_transformation,[],[f767]) ).
thf(f767,plain,
! [X0: set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat] :
( ! [X3: set_Pr1986765409at_nat,X4: set_Pr1986765409at_nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),X0,X3),X4)),X3) )
=> ( ! [X5: set_Pr1986765409at_nat,X6: set_Pr1986765409at_nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),X0,X5),X6)),X6) )
=> ( ! [X7: set_Pr1986765409at_nat,X8: set_Pr1986765409at_nat,X9: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X7),X8) )
=> ( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X7),X9) )
=> ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X7),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),X0,X8),X9)) ) ) )
=> ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),X2) = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),X0,X1),X2) ) ) ) ),
inference(fool_elimination,[],[f766]) ).
thf(f766,plain,
! [X0: set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat] :
( ! [X3: set_Pr1986765409at_nat,X4: set_Pr1986765409at_nat] : vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),X0,X3),X4)),X3)
=> ( ! [X5: set_Pr1986765409at_nat,X6: set_Pr1986765409at_nat] : vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),X0,X5),X6)),X6)
=> ( ! [X7: set_Pr1986765409at_nat,X8: set_Pr1986765409at_nat,X9: set_Pr1986765409at_nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X7),X8)
=> ( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X7),X9)
=> vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X7),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),X0,X8),X9)) ) )
=> ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),X2) = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),X0,X1),X2) ) ) ) ),
inference(rectify,[],[f285]) ).
thf(f285,axiom,
! [X25: set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat,X5: set_Pr1986765409at_nat,X21: set_Pr1986765409at_nat] :
( ! [X4: set_Pr1986765409at_nat,X26: set_Pr1986765409at_nat] : vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),X25,X4),X26)),X4)
=> ( ! [X4: set_Pr1986765409at_nat,X26: set_Pr1986765409at_nat] : vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),X25,X4),X26)),X26)
=> ( ! [X4: set_Pr1986765409at_nat,X26: set_Pr1986765409at_nat,X43: set_Pr1986765409at_nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X4),X26)
=> ( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X4),X43)
=> vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X4),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),X25,X26),X43)) ) )
=> ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X5),X21) = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),X25,X5),X21) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_284_inf__unique) ).
thf(f6402,plain,
spl155_274,
inference(avatar_split_clause,[],[f2329,f6400]) ).
thf(f6400,plain,
( spl155_274
<=> ! [X2: nat,X0: nat > nat > nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X1),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),X0,X1),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK46,X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),X0,vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK47,X0)),vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK48,X0))) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),X0,vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK49,X0)),vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK50,X0))),vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK50,X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),X0,vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK51,X0)),vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK52,X0))),vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK51,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_274])]) ).
thf(f2329,plain,
! [X2: nat,X0: nat > nat > nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X1),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),X0,X1),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK46,X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),X0,vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK47,X0)),vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK48,X0))) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),X0,vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK49,X0)),vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK50,X0))),vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK50,X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),X0,vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK51,X0)),vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK52,X0))),vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK51,X0)) ) ),
inference(definition_unfolding,[],[f1896,f1646,f1646,f1646]) ).
thf(f1896,plain,
! [X2: nat,X0: nat > nat > nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X1),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),X0,X1),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK46,X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),X0,vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK47,X0)),vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK48,X0))) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),X0,vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK49,X0)),vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK50,X0))),vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK50,X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),X0,vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK51,X0)),vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK52,X0))),vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK51,X0)) ) ),
inference(cnf_transformation,[],[f1511]) ).
thf(f1511,plain,
! [X0: nat > nat > nat,X1: nat,X2: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X1),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),X0,X1),X2) )
| ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK46,X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),X0,vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK47,X0)),vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK48,X0))) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK46,X0)),vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK48,X0)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK46,X0)),vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK47,X0)) ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),X0,vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK49,X0)),vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK50,X0))),vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK50,X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),X0,vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK51,X0)),vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK52,X0))),vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK51,X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK46,sK47,sK48,sK49,sK50,sK51,sK52])],[f1507,f1510,f1509,f1508]) ).
thf(f1508,plain,
! [X0: nat > nat > nat] :
( ? [X3: nat,X4: nat,X5: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),X0,X4),X5)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X5) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X4) ) )
=> ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK46,X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),X0,vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK47,X0)),vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK48,X0))) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK46,X0)),vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK48,X0)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK46,X0)),vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK47,X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1509,plain,
! [X0: nat > nat > nat] :
( ? [X6: nat,X7: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),X0,X6),X7)),X7) )
=> ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),X0,vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK49,X0)),vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK50,X0))),vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK50,X0)) ) ),
introduced(choice_axiom,[]) ).
thf(f1510,plain,
! [X0: nat > nat > nat] :
( ? [X8: nat,X9: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),X0,X8),X9)),X8) )
=> ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),X0,vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK51,X0)),vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK52,X0))),vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK51,X0)) ) ),
introduced(choice_axiom,[]) ).
thf(f1507,plain,
! [X0: nat > nat > nat,X1: nat,X2: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X1),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),X0,X1),X2) )
| ? [X3: nat,X4: nat,X5: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),X0,X4),X5)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X5) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X4) ) )
| ? [X6: nat,X7: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),X0,X6),X7)),X7) )
| ? [X8: nat,X9: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),X0,X8),X9)),X8) ) ),
inference(rectify,[],[f1215]) ).
thf(f1215,plain,
! [X0: nat > nat > nat,X1: nat,X2: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X1),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),X0,X1),X2) )
| ? [X7: nat,X8: nat,X9: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X7),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),X0,X8),X9)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X7),X9) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X7),X8) ) )
| ? [X5: nat,X6: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),X0,X5),X6)),X6) )
| ? [X3: nat,X4: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),X0,X3),X4)),X3) ) ),
inference(flattening,[],[f1214]) ).
thf(f1214,plain,
! [X0: nat > nat > nat,X1: nat,X2: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X1),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),X0,X1),X2) )
| ? [X7: nat,X8: nat,X9: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X7),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),X0,X8),X9)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X7),X9) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X7),X8) ) )
| ? [X5: nat,X6: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),X0,X5),X6)),X6) )
| ? [X3: nat,X4: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),X0,X3),X4)),X3) ) ),
inference(ennf_transformation,[],[f765]) ).
thf(f765,plain,
! [X0: nat > nat > nat,X1: nat,X2: nat] :
( ! [X3: nat,X4: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),X0,X3),X4)),X3) )
=> ( ! [X5: nat,X6: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),X0,X5),X6)),X6) )
=> ( ! [X7: nat,X8: nat,X9: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X7),X8) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X7),X9) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X7),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),X0,X8),X9)) ) ) )
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X1),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),X0,X1),X2) ) ) ) ),
inference(fool_elimination,[],[f764]) ).
thf(f764,plain,
! [X0: nat > nat > nat,X1: nat,X2: nat] :
( ! [X3: nat,X4: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),X0,X3),X4)),X3)
=> ( ! [X5: nat,X6: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),X0,X5),X6)),X6)
=> ( ! [X7: nat,X8: nat,X9: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X7),X8)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X7),X9)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X7),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),X0,X8),X9)) ) )
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X1),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),X0,X1),X2) ) ) ) ),
inference(rectify,[],[f287]) ).
thf(f287,axiom,
! [X25: nat > nat > nat,X5: nat,X21: nat] :
( ! [X4: nat,X26: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),X25,X4),X26)),X4)
=> ( ! [X4: nat,X26: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),X25,X4),X26)),X26)
=> ( ! [X4: nat,X26: nat,X43: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X26)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X43)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),X25,X26),X43)) ) )
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X5),X21) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),X25,X5),X21) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_286_inf__unique) ).
thf(f6398,plain,
spl155_273,
inference(avatar_split_clause,[],[f2326,f6396]) ).
thf(f6396,plain,
( spl155_273
<=> ! [X2: set_nat,X0: set_nat > set_nat > set_nat,X1: set_nat] :
( ( vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),X2) = vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),X0,X1),X2) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK39,X0)),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),X0,vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK40,X0)),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK41,X0))) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),X0,vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK42,X0)),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK43,X0))),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK43,X0)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),X0,vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK44,X0)),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK45,X0))),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK44,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_273])]) ).
thf(f2326,plain,
! [X2: set_nat,X0: set_nat > set_nat > set_nat,X1: set_nat] :
( ( vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),X2) = vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),X0,X1),X2) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK39,X0)),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),X0,vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK40,X0)),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK41,X0))) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),X0,vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK42,X0)),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK43,X0))),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK43,X0)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),X0,vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK44,X0)),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK45,X0))),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK44,X0)) ) ),
inference(definition_unfolding,[],[f1893,f1650,f1650,f1650]) ).
thf(f1893,plain,
! [X2: set_nat,X0: set_nat > set_nat > set_nat,X1: set_nat] :
( ( vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),X2) = vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),X0,X1),X2) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK39,X0)),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),X0,vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK40,X0)),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK41,X0))) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),X0,vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK42,X0)),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK43,X0))),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK43,X0)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),X0,vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK44,X0)),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK45,X0))),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK44,X0)) ) ),
inference(cnf_transformation,[],[f1506]) ).
thf(f1506,plain,
! [X0: set_nat > set_nat > set_nat,X1: set_nat,X2: set_nat] :
( ( vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),X2) = vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),X0,X1),X2) )
| ( ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK39,X0)),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),X0,vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK40,X0)),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK41,X0))) )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK39,X0)),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK41,X0)) )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK39,X0)),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK40,X0)) ) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),X0,vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK42,X0)),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK43,X0))),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK43,X0)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),X0,vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK44,X0)),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK45,X0))),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK44,X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK39,sK40,sK41,sK42,sK43,sK44,sK45])],[f1502,f1505,f1504,f1503]) ).
thf(f1503,plain,
! [X0: set_nat > set_nat > set_nat] :
( ? [X3: set_nat,X4: set_nat,X5: set_nat] :
( ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X3),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),X0,X4),X5)) )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X3),X5) )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X3),X4) ) )
=> ( ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK39,X0)),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),X0,vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK40,X0)),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK41,X0))) )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK39,X0)),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK41,X0)) )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK39,X0)),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK40,X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1504,plain,
! [X0: set_nat > set_nat > set_nat] :
( ? [X6: set_nat,X7: set_nat] : ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),X0,X6),X7)),X7) )
=> ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),X0,vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK42,X0)),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK43,X0))),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK43,X0)) ) ),
introduced(choice_axiom,[]) ).
thf(f1505,plain,
! [X0: set_nat > set_nat > set_nat] :
( ? [X8: set_nat,X9: set_nat] : ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),X0,X8),X9)),X8) )
=> ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),X0,vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK44,X0)),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK45,X0))),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK44,X0)) ) ),
introduced(choice_axiom,[]) ).
thf(f1502,plain,
! [X0: set_nat > set_nat > set_nat,X1: set_nat,X2: set_nat] :
( ( vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),X2) = vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),X0,X1),X2) )
| ? [X3: set_nat,X4: set_nat,X5: set_nat] :
( ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X3),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),X0,X4),X5)) )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X3),X5) )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X3),X4) ) )
| ? [X6: set_nat,X7: set_nat] : ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),X0,X6),X7)),X7) )
| ? [X8: set_nat,X9: set_nat] : ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),X0,X8),X9)),X8) ) ),
inference(rectify,[],[f1213]) ).
thf(f1213,plain,
! [X0: set_nat > set_nat > set_nat,X1: set_nat,X2: set_nat] :
( ( vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),X2) = vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),X0,X1),X2) )
| ? [X7: set_nat,X8: set_nat,X9: set_nat] :
( ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X7),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),X0,X8),X9)) )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X7),X9) )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X7),X8) ) )
| ? [X5: set_nat,X6: set_nat] : ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),X0,X5),X6)),X6) )
| ? [X3: set_nat,X4: set_nat] : ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),X0,X3),X4)),X3) ) ),
inference(flattening,[],[f1212]) ).
thf(f1212,plain,
! [X0: set_nat > set_nat > set_nat,X1: set_nat,X2: set_nat] :
( ( vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),X2) = vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),X0,X1),X2) )
| ? [X7: set_nat,X8: set_nat,X9: set_nat] :
( ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X7),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),X0,X8),X9)) )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X7),X9) )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X7),X8) ) )
| ? [X5: set_nat,X6: set_nat] : ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),X0,X5),X6)),X6) )
| ? [X3: set_nat,X4: set_nat] : ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),X0,X3),X4)),X3) ) ),
inference(ennf_transformation,[],[f763]) ).
thf(f763,plain,
! [X0: set_nat > set_nat > set_nat,X1: set_nat,X2: set_nat] :
( ! [X3: set_nat,X4: set_nat] : ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),X0,X3),X4)),X3) )
=> ( ! [X5: set_nat,X6: set_nat] : ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),X0,X5),X6)),X6) )
=> ( ! [X7: set_nat,X8: set_nat,X9: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X7),X8) )
=> ( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X7),X9) )
=> ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X7),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),X0,X8),X9)) ) ) )
=> ( vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),X2) = vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),X0,X1),X2) ) ) ) ),
inference(fool_elimination,[],[f762]) ).
thf(f762,plain,
! [X0: set_nat > set_nat > set_nat,X1: set_nat,X2: set_nat] :
( ! [X3: set_nat,X4: set_nat] : vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),X0,X3),X4)),X3)
=> ( ! [X5: set_nat,X6: set_nat] : vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),X0,X5),X6)),X6)
=> ( ! [X7: set_nat,X8: set_nat,X9: set_nat] :
( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X7),X8)
=> ( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X7),X9)
=> vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X7),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),X0,X8),X9)) ) )
=> ( vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),X2) = vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),X0,X1),X2) ) ) ) ),
inference(rectify,[],[f286]) ).
thf(f286,axiom,
! [X25: set_nat > set_nat > set_nat,X5: set_nat,X21: set_nat] :
( ! [X4: set_nat,X26: set_nat] : vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),X25,X4),X26)),X4)
=> ( ! [X4: set_nat,X26: set_nat] : vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),X25,X4),X26)),X26)
=> ( ! [X4: set_nat,X26: set_nat,X43: set_nat] :
( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X4),X26)
=> ( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X4),X43)
=> vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X4),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),X25,X26),X43)) ) )
=> ( vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X5),X21) = vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),X25,X5),X21) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_285_inf__unique) ).
thf(f6390,plain,
spl155_272,
inference(avatar_split_clause,[],[f2338,f6388]) ).
thf(f2338,plain,
! [X2: nat,X0: product_prod_nat_nat > a,X1: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,X0),X1),X2)) )
| ( $true != vAPP(sTfun(product_prod_nat_nat,a),$o,vAPP(sTfun(sTfun(product_prod_nat_nat,a),set_nat),sTfun(sTfun(product_prod_nat_nat,a),$o),vAPP(sTfun(set_nat,$o),sTfun(sTfun(sTfun(product_prod_nat_nat,a),set_nat),sTfun(sTfun(product_prod_nat_nat,a),$o)),bCOMB,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB)))))),v_a),X0) ) ),
inference(definition_unfolding,[],[f1904,f2100]) ).
thf(f1904,plain,
! [X2: nat,X0: product_prod_nat_nat > a,X1: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,X0),X1),X2)) )
| ( $true != vAPP(sTfun(product_prod_nat_nat,a),$o,edmond1517640972ysis_a,X0) ) ),
inference(cnf_transformation,[],[f1220]) ).
thf(f1220,plain,
! [X0: product_prod_nat_nat > a,X1: nat,X2: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,X0),X1),X2)) )
| ( $true != vAPP(sTfun(product_prod_nat_nat,a),$o,edmond1517640972ysis_a,X0) ) ),
inference(ennf_transformation,[],[f771]) ).
thf(f771,plain,
! [X0: product_prod_nat_nat > a,X1: nat,X2: nat] :
( ( $true = vAPP(sTfun(product_prod_nat_nat,a),$o,edmond1517640972ysis_a,X0) )
=> ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,X0),X1),X2)) ) ),
inference(fool_elimination,[],[f770]) ).
thf(f770,plain,
! [X0: product_prod_nat_nat > a,X1: nat,X2: nat] :
( vAPP(sTfun(product_prod_nat_nat,a),$o,edmond1517640972ysis_a,X0)
=> vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,X0),X1),X2)) ),
inference(rectify,[],[f189]) ).
thf(f189,axiom,
! [X9: product_prod_nat_nat > a,X10: nat,X11: nat] :
( vAPP(sTfun(product_prod_nat_nat,a),$o,edmond1517640972ysis_a,X9)
=> vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,X9),X10),X11)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_ek__analysis_Ofinite__spEdges) ).
thf(f6358,plain,
( spl155_271
| ~ spl155_245
| ~ spl155_255 ),
inference(avatar_split_clause,[],[f6235,f6209,f6127,f6356]) ).
thf(f6356,plain,
( spl155_271
<=> ! [X0: set_nat] : ( vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),incoming_a2,c),X0)) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_271])]) ).
thf(f6235,plain,
( ! [X0: set_nat] : ( vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),incoming_a2,c),X0)) = $true )
| ~ spl155_245
| ~ spl155_255 ),
inference(trivial_inequality_removal,[],[f6228]) ).
thf(f6228,plain,
( ! [X0: set_nat] :
( ( $true != $true )
| ( vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),incoming_a2,c),X0)) = $true ) )
| ~ spl155_245
| ~ spl155_255 ),
inference(superposition,[],[f6210,f6129]) ).
thf(f6344,plain,
spl155_270,
inference(avatar_split_clause,[],[f2334,f6342]) ).
thf(f6342,plain,
( spl155_270
<=> ! [X2: set_Pr1986765409at_nat,X0: set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),X2) = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),X0,X1),X2) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK53,X0)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK54,X0)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),X0,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK56,X0)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK57,X0))),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK57,X0)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),X0,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK58,X0)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK59,X0))),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK58,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_270])]) ).
thf(f2334,plain,
! [X2: set_Pr1986765409at_nat,X0: set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),X2) = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),X0,X1),X2) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK53,X0)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK54,X0)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),X0,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK56,X0)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK57,X0))),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK57,X0)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),X0,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK58,X0)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK59,X0))),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK58,X0)) ) ),
inference(definition_unfolding,[],[f1897,f1656,f1656,f1656]) ).
thf(f1897,plain,
! [X2: set_Pr1986765409at_nat,X0: set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),X2) = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),X0,X1),X2) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK53,X0)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK54,X0)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),X0,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK56,X0)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK57,X0))),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK57,X0)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),X0,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK58,X0)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK59,X0))),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK58,X0)) ) ),
inference(cnf_transformation,[],[f1516]) ).
thf(f6340,plain,
spl155_269,
inference(avatar_split_clause,[],[f2333,f6338]) ).
thf(f6338,plain,
( spl155_269
<=> ! [X2: set_Pr1986765409at_nat,X0: set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),X2) = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),X0,X1),X2) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK53,X0)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK55,X0)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),X0,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK56,X0)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK57,X0))),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK57,X0)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),X0,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK58,X0)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK59,X0))),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK58,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_269])]) ).
thf(f2333,plain,
! [X2: set_Pr1986765409at_nat,X0: set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),X2) = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),X0,X1),X2) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK53,X0)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK55,X0)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),X0,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK56,X0)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK57,X0))),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK57,X0)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),X0,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK58,X0)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK59,X0))),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK58,X0)) ) ),
inference(definition_unfolding,[],[f1898,f1656,f1656,f1656]) ).
thf(f1898,plain,
! [X2: set_Pr1986765409at_nat,X0: set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),X2) = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),X0,X1),X2) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK53,X0)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK55,X0)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),X0,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK56,X0)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK57,X0))),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK57,X0)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),X0,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK58,X0)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK59,X0))),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),set_Pr1986765409at_nat,sK58,X0)) ) ),
inference(cnf_transformation,[],[f1516]) ).
thf(f6336,plain,
spl155_268,
inference(avatar_split_clause,[],[f2331,f6334]) ).
thf(f6334,plain,
( spl155_268
<=> ! [X2: nat,X0: nat > nat > nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X1),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),X0,X1),X2) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK46,X0)),vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK47,X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),X0,vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK49,X0)),vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK50,X0))),vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK50,X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),X0,vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK51,X0)),vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK52,X0))),vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK51,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_268])]) ).
thf(f2331,plain,
! [X2: nat,X0: nat > nat > nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X1),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),X0,X1),X2) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK46,X0)),vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK47,X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),X0,vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK49,X0)),vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK50,X0))),vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK50,X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),X0,vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK51,X0)),vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK52,X0))),vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK51,X0)) ) ),
inference(definition_unfolding,[],[f1894,f1646,f1646,f1646]) ).
thf(f1894,plain,
! [X2: nat,X0: nat > nat > nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X1),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),X0,X1),X2) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK46,X0)),vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK47,X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),X0,vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK49,X0)),vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK50,X0))),vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK50,X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),X0,vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK51,X0)),vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK52,X0))),vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK51,X0)) ) ),
inference(cnf_transformation,[],[f1511]) ).
thf(f6332,plain,
spl155_267,
inference(avatar_split_clause,[],[f2330,f6330]) ).
thf(f6330,plain,
( spl155_267
<=> ! [X2: nat,X0: nat > nat > nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X1),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),X0,X1),X2) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK46,X0)),vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK48,X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),X0,vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK49,X0)),vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK50,X0))),vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK50,X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),X0,vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK51,X0)),vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK52,X0))),vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK51,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_267])]) ).
thf(f2330,plain,
! [X2: nat,X0: nat > nat > nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X1),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),X0,X1),X2) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK46,X0)),vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK48,X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),X0,vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK49,X0)),vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK50,X0))),vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK50,X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),X0,vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK51,X0)),vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK52,X0))),vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK51,X0)) ) ),
inference(definition_unfolding,[],[f1895,f1646,f1646,f1646]) ).
thf(f1895,plain,
! [X2: nat,X0: nat > nat > nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X1),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),X0,X1),X2) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK46,X0)),vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK48,X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),X0,vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK49,X0)),vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK50,X0))),vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK50,X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),X0,vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK51,X0)),vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK52,X0))),vAPP(sTfun(nat,sTfun(nat,nat)),nat,sK51,X0)) ) ),
inference(cnf_transformation,[],[f1511]) ).
thf(f6328,plain,
spl155_266,
inference(avatar_split_clause,[],[f2328,f6326]) ).
thf(f6326,plain,
( spl155_266
<=> ! [X2: set_nat,X0: set_nat > set_nat > set_nat,X1: set_nat] :
( ( vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),X2) = vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),X0,X1),X2) )
| ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK39,X0)),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK40,X0)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),X0,vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK42,X0)),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK43,X0))),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK43,X0)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),X0,vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK44,X0)),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK45,X0))),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK44,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_266])]) ).
thf(f2328,plain,
! [X2: set_nat,X0: set_nat > set_nat > set_nat,X1: set_nat] :
( ( vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),X2) = vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),X0,X1),X2) )
| ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK39,X0)),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK40,X0)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),X0,vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK42,X0)),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK43,X0))),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK43,X0)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),X0,vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK44,X0)),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK45,X0))),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK44,X0)) ) ),
inference(definition_unfolding,[],[f1891,f1650,f1650,f1650]) ).
thf(f1891,plain,
! [X2: set_nat,X0: set_nat > set_nat > set_nat,X1: set_nat] :
( ( vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),X2) = vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),X0,X1),X2) )
| ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK39,X0)),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK40,X0)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),X0,vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK42,X0)),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK43,X0))),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK43,X0)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),X0,vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK44,X0)),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK45,X0))),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK44,X0)) ) ),
inference(cnf_transformation,[],[f1506]) ).
thf(f6324,plain,
spl155_265,
inference(avatar_split_clause,[],[f2327,f6322]) ).
thf(f6322,plain,
( spl155_265
<=> ! [X2: set_nat,X0: set_nat > set_nat > set_nat,X1: set_nat] :
( ( vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),X2) = vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),X0,X1),X2) )
| ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK39,X0)),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK41,X0)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),X0,vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK42,X0)),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK43,X0))),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK43,X0)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),X0,vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK44,X0)),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK45,X0))),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK44,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_265])]) ).
thf(f2327,plain,
! [X2: set_nat,X0: set_nat > set_nat > set_nat,X1: set_nat] :
( ( vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),X2) = vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),X0,X1),X2) )
| ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK39,X0)),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK41,X0)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),X0,vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK42,X0)),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK43,X0))),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK43,X0)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),X0,vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK44,X0)),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK45,X0))),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK44,X0)) ) ),
inference(definition_unfolding,[],[f1892,f1650,f1650,f1650]) ).
thf(f1892,plain,
! [X2: set_nat,X0: set_nat > set_nat > set_nat,X1: set_nat] :
( ( vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),X2) = vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),X0,X1),X2) )
| ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK39,X0)),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK41,X0)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),X0,vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK42,X0)),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK43,X0))),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK43,X0)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),X0,vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK44,X0)),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK45,X0))),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),set_nat,sK44,X0)) ) ),
inference(cnf_transformation,[],[f1506]) ).
thf(f6312,plain,
( spl155_264
| ~ spl155_245
| ~ spl155_254 ),
inference(avatar_split_clause,[],[f6227,f6205,f6127,f6310]) ).
thf(f6310,plain,
( spl155_264
<=> ! [X0: set_nat] : ( vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),outgoing_a2,c),X0)) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_264])]) ).
thf(f6227,plain,
( ! [X0: set_nat] : ( vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),outgoing_a2,c),X0)) = $true )
| ~ spl155_245
| ~ spl155_254 ),
inference(trivial_inequality_removal,[],[f6220]) ).
thf(f6220,plain,
( ! [X0: set_nat] :
( ( $true != $true )
| ( vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),outgoing_a2,c),X0)) = $true ) )
| ~ spl155_245
| ~ spl155_254 ),
inference(superposition,[],[f6206,f6129]) ).
thf(f6304,plain,
spl155_263,
inference(avatar_split_clause,[],[f2142,f6302]) ).
thf(f6302,plain,
( spl155_263
<=> ! [X0: product_prod_nat_nat > a] :
( ( $true = vAPP(sTfun(product_prod_nat_nat,a),$o,vAPP(sTfun(sTfun(product_prod_nat_nat,a),set_nat),sTfun(sTfun(product_prod_nat_nat,a),$o),vAPP(sTfun(set_nat,$o),sTfun(sTfun(sTfun(product_prod_nat_nat,a),set_nat),sTfun(sTfun(product_prod_nat_nat,a),$o)),bCOMB,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB)))))),v_a),X0) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_263])]) ).
thf(f2142,plain,
! [X0: product_prod_nat_nat > a] :
( ( $true = vAPP(sTfun(product_prod_nat_nat,a),$o,vAPP(sTfun(sTfun(product_prod_nat_nat,a),set_nat),sTfun(sTfun(product_prod_nat_nat,a),$o),vAPP(sTfun(set_nat,$o),sTfun(sTfun(sTfun(product_prod_nat_nat,a),set_nat),sTfun(sTfun(product_prod_nat_nat,a),$o)),bCOMB,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB)))))),v_a),X0) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) ) ),
inference(definition_unfolding,[],[f1681,f2099]) ).
thf(f1681,plain,
! [X0: product_prod_nat_nat > a] :
( ( $true = vAPP(sTfun(product_prod_nat_nat,a),$o,finite_Graph_a,X0) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) ) ),
inference(cnf_transformation,[],[f1078]) ).
thf(f1078,plain,
! [X0: product_prod_nat_nat > a] :
( ( $true = vAPP(sTfun(product_prod_nat_nat,a),$o,finite_Graph_a,X0) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) ) ),
inference(ennf_transformation,[],[f457]) ).
thf(f457,plain,
! [X0: product_prod_nat_nat > a] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) )
=> ( $true = vAPP(sTfun(product_prod_nat_nat,a),$o,finite_Graph_a,X0) ) ),
inference(fool_elimination,[],[f456]) ).
thf(f456,plain,
! [X0: product_prod_nat_nat > a] :
( vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0))
=> vAPP(sTfun(product_prod_nat_nat,a),$o,finite_Graph_a,X0) ),
inference(rectify,[],[f187]) ).
thf(f187,axiom,
! [X9: product_prod_nat_nat > a] :
( vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X9))
=> vAPP(sTfun(product_prod_nat_nat,a),$o,finite_Graph_a,X9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_Graph_OFinite__Graph__EI) ).
thf(f6300,plain,
spl155_262,
inference(avatar_split_clause,[],[f2135,f6298]) ).
thf(f6298,plain,
( spl155_262
<=> ! [X0: product_prod_nat_nat > a] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) )
| ( $true != vAPP(sTfun(product_prod_nat_nat,a),$o,vAPP(sTfun(sTfun(product_prod_nat_nat,a),set_nat),sTfun(sTfun(product_prod_nat_nat,a),$o),vAPP(sTfun(set_nat,$o),sTfun(sTfun(sTfun(product_prod_nat_nat,a),set_nat),sTfun(sTfun(product_prod_nat_nat,a),$o)),bCOMB,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB)))))),v_a),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_262])]) ).
thf(f2135,plain,
! [X0: product_prod_nat_nat > a] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) )
| ( $true != vAPP(sTfun(product_prod_nat_nat,a),$o,vAPP(sTfun(sTfun(product_prod_nat_nat,a),set_nat),sTfun(sTfun(product_prod_nat_nat,a),$o),vAPP(sTfun(set_nat,$o),sTfun(sTfun(sTfun(product_prod_nat_nat,a),set_nat),sTfun(sTfun(product_prod_nat_nat,a),$o)),bCOMB,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB)))))),v_a),X0) ) ),
inference(definition_unfolding,[],[f1674,f2099]) ).
thf(f1674,plain,
! [X0: product_prod_nat_nat > a] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) )
| ( $true != vAPP(sTfun(product_prod_nat_nat,a),$o,finite_Graph_a,X0) ) ),
inference(cnf_transformation,[],[f1071]) ).
thf(f1071,plain,
! [X0: product_prod_nat_nat > a] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) )
| ( $true != vAPP(sTfun(product_prod_nat_nat,a),$o,finite_Graph_a,X0) ) ),
inference(ennf_transformation,[],[f443]) ).
thf(f443,plain,
! [X0: product_prod_nat_nat > a] :
( ( $true = vAPP(sTfun(product_prod_nat_nat,a),$o,finite_Graph_a,X0) )
=> ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) ) ),
inference(fool_elimination,[],[f442]) ).
thf(f442,plain,
! [X0: product_prod_nat_nat > a] :
( vAPP(sTfun(product_prod_nat_nat,a),$o,finite_Graph_a,X0)
=> vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) ),
inference(rectify,[],[f188]) ).
thf(f188,axiom,
! [X9: product_prod_nat_nat > a] :
( vAPP(sTfun(product_prod_nat_nat,a),$o,finite_Graph_a,X9)
=> vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X9)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_Finite__Graph_Ofinite__E) ).
thf(f6296,plain,
spl155_261,
inference(avatar_split_clause,[],[f2131,f6294]) ).
thf(f6294,plain,
( spl155_261
<=> ! [X0: product_prod_nat_nat > a] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,X0)) )
| ( $true != vAPP(sTfun(product_prod_nat_nat,a),$o,vAPP(sTfun(sTfun(product_prod_nat_nat,a),set_nat),sTfun(sTfun(product_prod_nat_nat,a),$o),vAPP(sTfun(set_nat,$o),sTfun(sTfun(sTfun(product_prod_nat_nat,a),set_nat),sTfun(sTfun(product_prod_nat_nat,a),$o)),bCOMB,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB)))))),v_a),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_261])]) ).
thf(f2131,plain,
! [X0: product_prod_nat_nat > a] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,X0)) )
| ( $true != vAPP(sTfun(product_prod_nat_nat,a),$o,vAPP(sTfun(sTfun(product_prod_nat_nat,a),set_nat),sTfun(sTfun(product_prod_nat_nat,a),$o),vAPP(sTfun(set_nat,$o),sTfun(sTfun(sTfun(product_prod_nat_nat,a),set_nat),sTfun(sTfun(product_prod_nat_nat,a),$o)),bCOMB,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB)))))),v_a),X0) ) ),
inference(definition_unfolding,[],[f1670,f2100]) ).
thf(f1670,plain,
! [X0: product_prod_nat_nat > a] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,X0)) )
| ( $true != vAPP(sTfun(product_prod_nat_nat,a),$o,edmond1517640972ysis_a,X0) ) ),
inference(cnf_transformation,[],[f1067]) ).
thf(f1067,plain,
! [X0: product_prod_nat_nat > a] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,X0)) )
| ( $true != vAPP(sTfun(product_prod_nat_nat,a),$o,edmond1517640972ysis_a,X0) ) ),
inference(ennf_transformation,[],[f435]) ).
thf(f435,plain,
! [X0: product_prod_nat_nat > a] :
( ( $true = vAPP(sTfun(product_prod_nat_nat,a),$o,edmond1517640972ysis_a,X0) )
=> ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,X0)) ) ),
inference(fool_elimination,[],[f434]) ).
thf(f434,plain,
! [X0: product_prod_nat_nat > a] :
( vAPP(sTfun(product_prod_nat_nat,a),$o,edmond1517640972ysis_a,X0)
=> vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,X0)) ),
inference(rectify,[],[f190]) ).
thf(f190,axiom,
! [X9: product_prod_nat_nat > a] :
( vAPP(sTfun(product_prod_nat_nat,a),$o,edmond1517640972ysis_a,X9)
=> vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,X9)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_ek__analysis_Ofinite__uE) ).
thf(f6268,plain,
spl155_260,
inference(avatar_split_clause,[],[f2219,f6266]) ).
thf(f2219,plain,
! [X0: set_nat,X1: nat] :
( ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,vAPP(set_nat,nat,vAPP(nat,sTfun(set_nat,nat),sK23,X1),X0)),X0) )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X1),X0) )
| ( $true != vAPP(set_nat,$o,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB))))),X0) ) ),
inference(definition_unfolding,[],[f1770,f2098]) ).
thf(f1770,plain,
! [X0: set_nat,X1: nat] :
( ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,vAPP(set_nat,nat,vAPP(nat,sTfun(set_nat,nat),sK23,X1),X0)),X0) )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X1),X0) )
| ( $true != vAPP(set_nat,$o,finite_finite_nat,X0) ) ),
inference(cnf_transformation,[],[f1476]) ).
thf(f6264,plain,
spl155_259,
inference(avatar_split_clause,[],[f2216,f6262]) ).
thf(f2216,plain,
! [X0: set_nat,X1: nat] :
( ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,vAPP(set_nat,nat,vAPP(nat,sTfun(set_nat,nat),sK22,X1),X0)),X0) )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X1),X0) )
| ( $true != vAPP(set_nat,$o,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB))))),X0) ) ),
inference(definition_unfolding,[],[f1767,f2098]) ).
thf(f1767,plain,
! [X0: set_nat,X1: nat] :
( ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,vAPP(set_nat,nat,vAPP(nat,sTfun(set_nat,nat),sK22,X1),X0)),X0) )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X1),X0) )
| ( $true != vAPP(set_nat,$o,finite_finite_nat,X0) ) ),
inference(cnf_transformation,[],[f1474]) ).
thf(f6260,plain,
spl155_258,
inference(avatar_split_clause,[],[f2481,f6257]) ).
thf(f2481,plain,
$true = vAPP(sTfun(product_prod_nat_nat,a),$o,vAPP(sTfun(sTfun(product_prod_nat_nat,a),set_nat),sTfun(sTfun(product_prod_nat_nat,a),$o),vAPP(sTfun(set_nat,$o),sTfun(sTfun(sTfun(product_prod_nat_nat,a),set_nat),sTfun(sTfun(product_prod_nat_nat,a),$o)),bCOMB,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB)))))),v_a),c),
inference(definition_unfolding,[],[f2086,f2100]) ).
thf(f2086,plain,
vAPP(sTfun(product_prod_nat_nat,a),$o,edmond1517640972ysis_a,c) = $true,
inference(cnf_transformation,[],[f1013]) ).
thf(f1013,plain,
vAPP(sTfun(product_prod_nat_nat,a),$o,edmond1517640972ysis_a,c) = $true,
inference(fool_elimination,[],[f1012]) ).
thf(f1012,plain,
vAPP(sTfun(product_prod_nat_nat,a),$o,edmond1517640972ysis_a,c),
inference(rectify,[],[f3]) ).
thf(f3,axiom,
vAPP(sTfun(product_prod_nat_nat,a),$o,edmond1517640972ysis_a,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_ek__analysis__axioms) ).
thf(f6219,plain,
spl155_257,
inference(avatar_split_clause,[],[f2228,f6217]) ).
thf(f2228,plain,
! [X0: product_prod_nat_nat > a,X1: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),outgoing_a,X0),X1)) )
| ( $true != vAPP(set_nat,$o,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB))))),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0)) ) ),
inference(definition_unfolding,[],[f1781,f2098]) ).
thf(f1781,plain,
! [X0: product_prod_nat_nat > a,X1: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),outgoing_a,X0),X1)) )
| ( $true != vAPP(set_nat,$o,finite_finite_nat,vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0)) ) ),
inference(cnf_transformation,[],[f1138]) ).
thf(f1138,plain,
! [X0: product_prod_nat_nat > a,X1: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),outgoing_a,X0),X1)) )
| ( $true != vAPP(set_nat,$o,finite_finite_nat,vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0)) ) ),
inference(ennf_transformation,[],[f589]) ).
thf(f589,plain,
! [X0: product_prod_nat_nat > a,X1: nat] :
( ( $true = vAPP(set_nat,$o,finite_finite_nat,vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0)) )
=> ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),outgoing_a,X0),X1)) ) ),
inference(fool_elimination,[],[f588]) ).
thf(f588,plain,
! [X0: product_prod_nat_nat > a,X1: nat] :
( vAPP(set_nat,$o,finite_finite_nat,vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0))
=> vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),outgoing_a,X0),X1)) ),
inference(rectify,[],[f230]) ).
thf(f230,axiom,
! [X9: product_prod_nat_nat > a,X1: nat] :
( vAPP(set_nat,$o,finite_finite_nat,vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X9))
=> vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),outgoing_a,X9),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_Graph_Ofinite__outgoing) ).
thf(f6215,plain,
spl155_256,
inference(avatar_split_clause,[],[f2227,f6213]) ).
thf(f2227,plain,
! [X0: product_prod_nat_nat > a,X1: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),incoming_a,X0),X1)) )
| ( $true != vAPP(set_nat,$o,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB))))),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0)) ) ),
inference(definition_unfolding,[],[f1780,f2098]) ).
thf(f1780,plain,
! [X0: product_prod_nat_nat > a,X1: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),incoming_a,X0),X1)) )
| ( $true != vAPP(set_nat,$o,finite_finite_nat,vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0)) ) ),
inference(cnf_transformation,[],[f1137]) ).
thf(f1137,plain,
! [X0: product_prod_nat_nat > a,X1: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),incoming_a,X0),X1)) )
| ( $true != vAPP(set_nat,$o,finite_finite_nat,vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0)) ) ),
inference(ennf_transformation,[],[f587]) ).
thf(f587,plain,
! [X0: product_prod_nat_nat > a,X1: nat] :
( ( $true = vAPP(set_nat,$o,finite_finite_nat,vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0)) )
=> ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),incoming_a,X0),X1)) ) ),
inference(fool_elimination,[],[f586]) ).
thf(f586,plain,
! [X0: product_prod_nat_nat > a,X1: nat] :
( vAPP(set_nat,$o,finite_finite_nat,vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0))
=> vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),incoming_a,X0),X1)) ),
inference(rectify,[],[f231]) ).
thf(f231,axiom,
! [X9: product_prod_nat_nat > a,X1: nat] :
( vAPP(set_nat,$o,finite_finite_nat,vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X9))
=> vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),incoming_a,X9),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_Graph_Ofinite__incoming) ).
thf(f6211,plain,
spl155_255,
inference(avatar_split_clause,[],[f2226,f6209]) ).
thf(f2226,plain,
! [X0: product_prod_nat_nat > a,X1: set_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),incoming_a2,X0),X1)) )
| ( $true != vAPP(set_nat,$o,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB))))),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0)) ) ),
inference(definition_unfolding,[],[f1779,f2098]) ).
thf(f1779,plain,
! [X0: product_prod_nat_nat > a,X1: set_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),incoming_a2,X0),X1)) )
| ( $true != vAPP(set_nat,$o,finite_finite_nat,vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0)) ) ),
inference(cnf_transformation,[],[f1136]) ).
thf(f1136,plain,
! [X0: product_prod_nat_nat > a,X1: set_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),incoming_a2,X0),X1)) )
| ( $true != vAPP(set_nat,$o,finite_finite_nat,vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0)) ) ),
inference(ennf_transformation,[],[f585]) ).
thf(f585,plain,
! [X0: product_prod_nat_nat > a,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,finite_finite_nat,vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0)) )
=> ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),incoming_a2,X0),X1)) ) ),
inference(fool_elimination,[],[f584]) ).
thf(f584,plain,
! [X0: product_prod_nat_nat > a,X1: set_nat] :
( vAPP(set_nat,$o,finite_finite_nat,vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0))
=> vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),incoming_a2,X0),X1)) ),
inference(rectify,[],[f233]) ).
thf(f233,axiom,
! [X9: product_prod_nat_nat > a,X0: set_nat] :
( vAPP(set_nat,$o,finite_finite_nat,vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X9))
=> vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),incoming_a2,X9),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_Graph_Ofinite__incoming_H) ).
thf(f6207,plain,
spl155_254,
inference(avatar_split_clause,[],[f2225,f6205]) ).
thf(f2225,plain,
! [X0: product_prod_nat_nat > a,X1: set_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),outgoing_a2,X0),X1)) )
| ( $true != vAPP(set_nat,$o,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB))))),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0)) ) ),
inference(definition_unfolding,[],[f1778,f2098]) ).
thf(f1778,plain,
! [X0: product_prod_nat_nat > a,X1: set_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),outgoing_a2,X0),X1)) )
| ( $true != vAPP(set_nat,$o,finite_finite_nat,vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0)) ) ),
inference(cnf_transformation,[],[f1135]) ).
thf(f1135,plain,
! [X0: product_prod_nat_nat > a,X1: set_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),outgoing_a2,X0),X1)) )
| ( $true != vAPP(set_nat,$o,finite_finite_nat,vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0)) ) ),
inference(ennf_transformation,[],[f583]) ).
thf(f583,plain,
! [X0: product_prod_nat_nat > a,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,finite_finite_nat,vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0)) )
=> ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),outgoing_a2,X0),X1)) ) ),
inference(fool_elimination,[],[f582]) ).
thf(f582,plain,
! [X0: product_prod_nat_nat > a,X1: set_nat] :
( vAPP(set_nat,$o,finite_finite_nat,vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0))
=> vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),outgoing_a2,X0),X1)) ),
inference(rectify,[],[f232]) ).
thf(f232,axiom,
! [X9: product_prod_nat_nat > a,X0: set_nat] :
( vAPP(set_nat,$o,finite_finite_nat,vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X9))
=> vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),outgoing_a2,X9),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_Graph_Ofinite__outgoing_H) ).
thf(f6197,plain,
spl155_253,
inference(avatar_split_clause,[],[f2191,f6195]) ).
thf(f6195,plain,
( spl155_253
<=> ! [X0: nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB))))),vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK14,X1),X0)) )
| ( $true != vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_253])]) ).
thf(f2191,plain,
! [X0: nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB))))),vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK14,X1),X0)) )
| ( $true != vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,X1),X0) ) ),
inference(definition_unfolding,[],[f1738,f2098]) ).
thf(f1738,plain,
! [X0: nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,finite_finite_nat,vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK14,X1),X0)) )
| ( $true != vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,X1),X0) ) ),
inference(cnf_transformation,[],[f1456]) ).
thf(f1456,plain,
! [X0: nat,X1: set_nat] :
( ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,finite_card_nat,vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK14,X1),X0))),X0) )
& ( $true = vAPP(set_nat,$o,finite_finite_nat,vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK14,X1),X0)) )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK14,X1),X0)),X1) ) )
| ( $true != vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,X1),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f1454,f1455]) ).
thf(f1455,plain,
! [X0: nat,X1: set_nat] :
( ? [X2: set_nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,finite_card_nat,X2)),X0) )
& ( vAPP(set_nat,$o,finite_finite_nat,X2) = $true )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X1) ) )
=> ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,finite_card_nat,vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK14,X1),X0))),X0) )
& ( $true = vAPP(set_nat,$o,finite_finite_nat,vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK14,X1),X0)) )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK14,X1),X0)),X1) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1454,plain,
! [X0: nat,X1: set_nat] :
( ? [X2: set_nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,finite_card_nat,X2)),X0) )
& ( vAPP(set_nat,$o,finite_finite_nat,X2) = $true )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X1) ) )
| ( $true != vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,X1),X0) ) ),
inference(rectify,[],[f1453]) ).
thf(f1453,plain,
! [X1: nat,X0: set_nat] :
( ? [X2: set_nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,finite_card_nat,X2)),X1) )
& ( vAPP(set_nat,$o,finite_finite_nat,X2) = $true )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X0) ) )
| ( $true != vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,X0),X1) ) ),
inference(nnf_transformation,[],[f1428]) ).
thf(f1428,plain,
! [X1: nat,X0: set_nat] :
( ? [X2: set_nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,finite_card_nat,X2)),X1) )
& ( vAPP(set_nat,$o,finite_finite_nat,X2) = $true )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X0) ) )
| ( $true != vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,X0),X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f6193,plain,
( spl155_252
| ~ spl155_244
| ~ spl155_246 ),
inference(avatar_split_clause,[],[f6139,f6132,f6123,f6191]) ).
thf(f6191,plain,
( spl155_252
<=> ! [X0: list_nat] : ( vAPP(list_nat,set_nat,set_nat2,X0) = vAPP(list_nat,set_nat,set_nat2,vAPP(set_nat,list_nat,sK8,vAPP(list_nat,set_nat,set_nat2,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_252])]) ).
thf(f6139,plain,
( ! [X0: list_nat] : ( vAPP(list_nat,set_nat,set_nat2,X0) = vAPP(list_nat,set_nat,set_nat2,vAPP(set_nat,list_nat,sK8,vAPP(list_nat,set_nat,set_nat2,X0))) )
| ~ spl155_244
| ~ spl155_246 ),
inference(trivial_inequality_removal,[],[f6136]) ).
thf(f6136,plain,
( ! [X0: list_nat] :
( ( $true != $true )
| ( vAPP(list_nat,set_nat,set_nat2,X0) = vAPP(list_nat,set_nat,set_nat2,vAPP(set_nat,list_nat,sK8,vAPP(list_nat,set_nat,set_nat2,X0))) ) )
| ~ spl155_244
| ~ spl155_246 ),
inference(superposition,[],[f6133,f6124]) ).
thf(f6177,plain,
spl155_251,
inference(avatar_split_clause,[],[f2143,f6175]) ).
thf(f6175,plain,
( spl155_251
<=> ! [X0: product_prod_nat_nat > a] :
( ( $true = vAPP(set_nat,$o,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB))))),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_251])]) ).
thf(f2143,plain,
! [X0: product_prod_nat_nat > a] :
( ( $true = vAPP(set_nat,$o,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB))))),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) ) ),
inference(definition_unfolding,[],[f1682,f2098]) ).
thf(f1682,plain,
! [X0: product_prod_nat_nat > a] :
( ( $true = vAPP(set_nat,$o,finite_finite_nat,vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) ) ),
inference(cnf_transformation,[],[f1079]) ).
thf(f1079,plain,
! [X0: product_prod_nat_nat > a] :
( ( $true = vAPP(set_nat,$o,finite_finite_nat,vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) ) ),
inference(ennf_transformation,[],[f459]) ).
thf(f459,plain,
! [X0: product_prod_nat_nat > a] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) )
=> ( $true = vAPP(set_nat,$o,finite_finite_nat,vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0)) ) ),
inference(fool_elimination,[],[f458]) ).
thf(f458,plain,
! [X0: product_prod_nat_nat > a] :
( vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0))
=> vAPP(set_nat,$o,finite_finite_nat,vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0)) ),
inference(rectify,[],[f228]) ).
thf(f228,axiom,
! [X9: product_prod_nat_nat > a] :
( vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X9))
=> vAPP(set_nat,$o,finite_finite_nat,vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X9)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_Graph_OEfin__imp__Vfin) ).
thf(f6173,plain,
spl155_250,
inference(avatar_split_clause,[],[f2141,f6171]) ).
thf(f2141,plain,
! [X0: product_prod_nat_nat > a] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) )
| ( $true != vAPP(set_nat,$o,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB))))),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0)) ) ),
inference(definition_unfolding,[],[f1680,f2098]) ).
thf(f1680,plain,
! [X0: product_prod_nat_nat > a] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) )
| ( $true != vAPP(set_nat,$o,finite_finite_nat,vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0)) ) ),
inference(cnf_transformation,[],[f1077]) ).
thf(f1077,plain,
! [X0: product_prod_nat_nat > a] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) )
| ( $true != vAPP(set_nat,$o,finite_finite_nat,vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0)) ) ),
inference(ennf_transformation,[],[f455]) ).
thf(f455,plain,
! [X0: product_prod_nat_nat > a] :
( ( $true = vAPP(set_nat,$o,finite_finite_nat,vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0)) )
=> ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) ) ),
inference(fool_elimination,[],[f454]) ).
thf(f454,plain,
! [X0: product_prod_nat_nat > a] :
( vAPP(set_nat,$o,finite_finite_nat,vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0))
=> vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) ),
inference(rectify,[],[f229]) ).
thf(f229,axiom,
! [X9: product_prod_nat_nat > a] :
( vAPP(set_nat,$o,finite_finite_nat,vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X9))
=> vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X9)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_Graph_OVfin__imp__Efin) ).
thf(f6164,plain,
spl155_249,
inference(avatar_split_clause,[],[f2182,f6162]) ).
thf(f2182,plain,
! [X0: set_nat,X1: nat] :
( ( vAPP(set_nat,nat,finite_card_nat,vAPP(set_nat,set_nat,vAPP(nat,sTfun(set_nat,set_nat),sK10,X1),X0)) = X1 )
| ( $true = vAPP(set_nat,$o,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB))))),X0) ) ),
inference(definition_unfolding,[],[f1727,f2098]) ).
thf(f1727,plain,
! [X0: set_nat,X1: nat] :
( ( vAPP(set_nat,nat,finite_card_nat,vAPP(set_nat,set_nat,vAPP(nat,sTfun(set_nat,set_nat),sK10,X1),X0)) = X1 )
| ( $true = vAPP(set_nat,$o,finite_finite_nat,X0) ) ),
inference(cnf_transformation,[],[f1446]) ).
thf(f6150,plain,
spl155_248,
inference(avatar_split_clause,[],[f2194,f6148]) ).
thf(f2194,plain,
! [X0: set_nat,X1: nat] :
( ( $true = vAPP(set_nat,$o,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB))))),X0) )
| ( $true = vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,X0),X1) ) ),
inference(definition_unfolding,[],[f1740,f2098]) ).
thf(f1740,plain,
! [X0: set_nat,X1: nat] :
( ( $true = vAPP(set_nat,$o,finite_finite_nat,X0) )
| ( $true = vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,X0),X1) ) ),
inference(cnf_transformation,[],[f1429]) ).
thf(f1429,plain,
! [X0: set_nat,X1: nat] :
( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,finite_card_nat,X0)),X1) )
& ( $true = vAPP(set_nat,$o,finite_finite_nat,X0) ) )
| ( $true = vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,X0),X1) ) ),
inference(definition_folding,[],[f1101,f1428]) ).
thf(f1101,plain,
! [X0: set_nat,X1: nat] :
( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,finite_card_nat,X0)),X1) )
& ( $true = vAPP(set_nat,$o,finite_finite_nat,X0) ) )
| ? [X2: set_nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,finite_card_nat,X2)),X1) )
& ( vAPP(set_nat,$o,finite_finite_nat,X2) = $true )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X0) ) ) ),
inference(flattening,[],[f1100]) ).
thf(f1100,plain,
! [X0: set_nat,X1: nat] :
( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,finite_card_nat,X0)),X1) )
& ( $true = vAPP(set_nat,$o,finite_finite_nat,X0) ) )
| ? [X2: set_nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,finite_card_nat,X2)),X1) )
& ( vAPP(set_nat,$o,finite_finite_nat,X2) = $true )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X0) ) ) ),
inference(ennf_transformation,[],[f545]) ).
thf(f545,plain,
! [X0: set_nat,X1: nat] :
( ! [X2: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X0) )
=> ( ( vAPP(set_nat,$o,finite_finite_nat,X2) = $true )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,finite_card_nat,X2)),X1) ) ) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,finite_card_nat,X0)),X1) )
& ( $true = vAPP(set_nat,$o,finite_finite_nat,X0) ) ) ),
inference(fool_elimination,[],[f544]) ).
thf(f544,plain,
! [X0: set_nat,X1: nat] :
( ! [X2: set_nat] :
( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X0)
=> ( vAPP(set_nat,$o,finite_finite_nat,X2)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,finite_card_nat,X2)),X1) ) )
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,finite_card_nat,X0)),X1)
& vAPP(set_nat,$o,finite_finite_nat,X0) ) ),
inference(rectify,[],[f336]) ).
thf(f336,axiom,
! [X38: set_nat,X30: nat] :
( ! [X50: set_nat] :
( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X50),X38)
=> ( vAPP(set_nat,$o,finite_finite_nat,X50)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,finite_card_nat,X50)),X30) ) )
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,finite_card_nat,X38)),X30)
& vAPP(set_nat,$o,finite_finite_nat,X38) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_335_finite__if__finite__subsets__card__bdd) ).
thf(f6144,plain,
spl155_247,
inference(avatar_split_clause,[],[f2154,f6142]) ).
thf(f2154,plain,
! [X0: nat] : ( $true = vAPP(set_nat,$o,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB))))),vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),adjacent_nodes_a,c),X0)) ),
inference(definition_unfolding,[],[f1694,f2098]) ).
thf(f1694,plain,
! [X0: nat] : ( $true = vAPP(set_nat,$o,finite_finite_nat,vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),adjacent_nodes_a,c),X0)) ),
inference(cnf_transformation,[],[f483]) ).
thf(f483,plain,
! [X0: nat] : ( $true = vAPP(set_nat,$o,finite_finite_nat,vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),adjacent_nodes_a,c),X0)) ),
inference(fool_elimination,[],[f482]) ).
thf(f482,plain,
! [X0: nat] : vAPP(set_nat,$o,finite_finite_nat,vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),adjacent_nodes_a,c),X0)),
inference(rectify,[],[f218]) ).
thf(f218,axiom,
! [X1: nat] : vAPP(set_nat,$o,finite_finite_nat,vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),adjacent_nodes_a,c),X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_adjacent__nodes__finite) ).
thf(f6134,plain,
spl155_246,
inference(avatar_split_clause,[],[f2129,f6132]) ).
thf(f2129,plain,
! [X0: set_nat] :
( ( vAPP(list_nat,set_nat,set_nat2,vAPP(set_nat,list_nat,sK8,X0)) = X0 )
| ( $true != vAPP(set_nat,$o,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB))))),X0) ) ),
inference(definition_unfolding,[],[f1667,f2098]) ).
thf(f1667,plain,
! [X0: set_nat] :
( ( vAPP(list_nat,set_nat,set_nat2,vAPP(set_nat,list_nat,sK8,X0)) = X0 )
| ( $true != vAPP(set_nat,$o,finite_finite_nat,X0) ) ),
inference(cnf_transformation,[],[f1442]) ).
thf(f1442,plain,
! [X0: set_nat] :
( ( vAPP(list_nat,set_nat,set_nat2,vAPP(set_nat,list_nat,sK8,X0)) = X0 )
| ( $true != vAPP(set_nat,$o,finite_finite_nat,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f1064,f1441]) ).
thf(f1441,plain,
! [X0: set_nat] :
( ? [X1: list_nat] : ( vAPP(list_nat,set_nat,set_nat2,X1) = X0 )
=> ( vAPP(list_nat,set_nat,set_nat2,vAPP(set_nat,list_nat,sK8,X0)) = X0 ) ),
introduced(choice_axiom,[]) ).
thf(f1064,plain,
! [X0: set_nat] :
( ? [X1: list_nat] : ( vAPP(list_nat,set_nat,set_nat2,X1) = X0 )
| ( $true != vAPP(set_nat,$o,finite_finite_nat,X0) ) ),
inference(ennf_transformation,[],[f429]) ).
thf(f429,plain,
! [X0: set_nat] :
( ( $true = vAPP(set_nat,$o,finite_finite_nat,X0) )
=> ? [X1: list_nat] : ( vAPP(list_nat,set_nat,set_nat2,X1) = X0 ) ),
inference(fool_elimination,[],[f428]) ).
thf(f428,plain,
! [X0: set_nat] :
( vAPP(set_nat,$o,finite_finite_nat,X0)
=> ? [X1: list_nat] : ( vAPP(list_nat,set_nat,set_nat2,X1) = X0 ) ),
inference(rectify,[],[f328]) ).
thf(f328,axiom,
! [X2: set_nat] :
( vAPP(set_nat,$o,finite_finite_nat,X2)
=> ? [X47: list_nat] : ( vAPP(list_nat,set_nat,set_nat2,X47) = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_327_finite__list) ).
thf(f6130,plain,
spl155_245,
inference(avatar_split_clause,[],[f2483,f6127]) ).
thf(f2483,plain,
$true = vAPP(set_nat,$o,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB))))),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,c)),
inference(definition_unfolding,[],[f2088,f2098]) ).
thf(f2088,plain,
vAPP(set_nat,$o,finite_finite_nat,vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,c)) = $true,
inference(cnf_transformation,[],[f1017]) ).
thf(f1017,plain,
vAPP(set_nat,$o,finite_finite_nat,vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,c)) = $true,
inference(fool_elimination,[],[f1016]) ).
thf(f1016,plain,
vAPP(set_nat,$o,finite_finite_nat,vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,c)),
inference(rectify,[],[f217]) ).
thf(f217,axiom,
vAPP(set_nat,$o,finite_finite_nat,vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_finite__V) ).
thf(f6125,plain,
spl155_244,
inference(avatar_split_clause,[],[f2145,f6123]) ).
thf(f2145,plain,
! [X0: list_nat] : ( $true = vAPP(set_nat,$o,vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB))))),vAPP(list_nat,set_nat,set_nat2,X0)) ),
inference(definition_unfolding,[],[f1684,f2098]) ).
thf(f1684,plain,
! [X0: list_nat] : ( $true = vAPP(set_nat,$o,finite_finite_nat,vAPP(list_nat,set_nat,set_nat2,X0)) ),
inference(cnf_transformation,[],[f463]) ).
thf(f463,plain,
! [X0: list_nat] : ( $true = vAPP(set_nat,$o,finite_finite_nat,vAPP(list_nat,set_nat,set_nat2,X0)) ),
inference(fool_elimination,[],[f462]) ).
thf(f462,plain,
! [X0: list_nat] : vAPP(set_nat,$o,finite_finite_nat,vAPP(list_nat,set_nat,set_nat2,X0)),
inference(rectify,[],[f205]) ).
thf(f205,axiom,
! [X40: list_nat] : vAPP(set_nat,$o,finite_finite_nat,vAPP(list_nat,set_nat,set_nat2,X40)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_List_Ofinite__set) ).
thf(f6049,plain,
( spl155_242
| ~ spl155_243
| ~ spl155_3
| ~ spl155_71
| ~ spl155_102 ),
inference(avatar_split_clause,[],[f3548,f3476,f3223,f2771,f6046,f6042]) ).
thf(f6046,plain,
( spl155_243
<=> ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p)) = vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,edges) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_243])]) ).
thf(f3548,plain,
( ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p)) != vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,edges) )
| ( edges = vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p) )
| ~ spl155_3
| ~ spl155_71
| ~ spl155_102 ),
inference(trivial_inequality_removal,[],[f3547]) ).
thf(f3547,plain,
( ( $true != $true )
| ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p)) != vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,edges) )
| ( edges = vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p) )
| ~ spl155_3
| ~ spl155_71
| ~ spl155_102 ),
inference(forward_demodulation,[],[f3544,f2772]) ).
thf(f3544,plain,
( ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p)) != vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,edges) )
| ( edges = vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p)) )
| ~ spl155_71
| ~ spl155_102 ),
inference(trivial_inequality_removal,[],[f3531]) ).
thf(f3531,plain,
( ( $true != $true )
| ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p)) != vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,edges) )
| ( edges = vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p)) )
| ~ spl155_71
| ~ spl155_102 ),
inference(superposition,[],[f3477,f3225]) ).
thf(f6020,plain,
spl155_241,
inference(avatar_split_clause,[],[f2546,f6018]) ).
thf(f6018,plain,
( spl155_241
<=> ! [X2: set_Pr1986765409at_nat > set_Pr1986765409at_nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X2,X0)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X2,X1)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X2,vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),set_Pr1986765409at_nat,sK124,X2))),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X2,vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),set_Pr1986765409at_nat,sK125,X2))) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_241])]) ).
thf(f2546,plain,
! [X2: set_Pr1986765409at_nat > set_Pr1986765409at_nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X2,X0)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X2,X1)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X2,vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),set_Pr1986765409at_nat,sK124,X2))),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X2,vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),set_Pr1986765409at_nat,sK125,X2))) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X1) ) ),
inference(equality_resolution,[],[f2448]) ).
thf(f2448,plain,
! [X2: set_Pr1986765409at_nat > set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X2,X0)),X3) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X2,vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),set_Pr1986765409at_nat,sK124,X2))),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X2,vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),set_Pr1986765409at_nat,sK125,X2))) )
| ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X2,X1) != X3 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X1) ) ),
inference(definition_unfolding,[],[f2045,f1656,f1656,f1656]) ).
thf(f2045,plain,
! [X2: set_Pr1986765409at_nat > set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X2,X0)),X3) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X2,vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),set_Pr1986765409at_nat,sK124,X2))),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X2,vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),set_Pr1986765409at_nat,sK125,X2))) )
| ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X2,X1) != X3 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1584]) ).
thf(f1584,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat > set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X2,X0)),X3) )
| ( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X2,vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),set_Pr1986765409at_nat,sK124,X2))),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X2,vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),set_Pr1986765409at_nat,sK125,X2))) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),set_Pr1986765409at_nat,sK124,X2)),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),set_Pr1986765409at_nat,sK125,X2)) ) )
| ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X2,X1) != X3 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK124,sK125])],[f1378,f1583]) ).
thf(f1583,plain,
! [X2: set_Pr1986765409at_nat > set_Pr1986765409at_nat] :
( ? [X4: set_Pr1986765409at_nat,X5: set_Pr1986765409at_nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X2,X4)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X2,X5)) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X4),X5) ) )
=> ( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X2,vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),set_Pr1986765409at_nat,sK124,X2))),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X2,vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),set_Pr1986765409at_nat,sK125,X2))) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),set_Pr1986765409at_nat,sK124,X2)),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),set_Pr1986765409at_nat,sK125,X2)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1378,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat > set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X2,X0)),X3) )
| ? [X4: set_Pr1986765409at_nat,X5: set_Pr1986765409at_nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X2,X4)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X2,X5)) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X4),X5) ) )
| ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X2,X1) != X3 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1) ) ),
inference(flattening,[],[f1377]) ).
thf(f1377,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat > set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X2,X0)),X3) )
| ? [X4: set_Pr1986765409at_nat,X5: set_Pr1986765409at_nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X2,X4)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X2,X5)) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X4),X5) ) )
| ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X2,X1) != X3 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1) ) ),
inference(ennf_transformation,[],[f959]) ).
thf(f959,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat > set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1) )
=> ( ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X2,X1) = X3 )
=> ( ! [X4: set_Pr1986765409at_nat,X5: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X4),X5) )
=> ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X2,X4)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X2,X5)) ) )
=> ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X2,X0)),X3) ) ) ) ),
inference(fool_elimination,[],[f958]) ).
thf(f958,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat > set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1)
=> ( ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X2,X1) = X3 )
=> ( ! [X4: set_Pr1986765409at_nat,X5: set_Pr1986765409at_nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X4),X5)
=> vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X2,X4)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X2,X5)) )
=> vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X2,X0)),X3) ) ) ),
inference(rectify,[],[f75]) ).
thf(f75,axiom,
! [X13: set_Pr1986765409at_nat,X12: set_Pr1986765409at_nat,X25: set_Pr1986765409at_nat > set_Pr1986765409at_nat,X9: set_Pr1986765409at_nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X13),X12)
=> ( ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X25,X12) = X9 )
=> ( ! [X4: set_Pr1986765409at_nat,X26: set_Pr1986765409at_nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X4),X26)
=> vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X25,X4)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X25,X26)) )
=> vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X25,X13)),X9) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_ord__le__eq__subst) ).
thf(f6016,plain,
spl155_240,
inference(avatar_split_clause,[],[f2544,f6014]) ).
thf(f6014,plain,
( spl155_240
<=> ! [X2: set_Pr1986765409at_nat > nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,nat,X2,X0)),vAPP(set_Pr1986765409at_nat,nat,X2,X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,nat,X2,vAPP(sTfun(set_Pr1986765409at_nat,nat),set_Pr1986765409at_nat,sK122,X2))),vAPP(set_Pr1986765409at_nat,nat,X2,vAPP(sTfun(set_Pr1986765409at_nat,nat),set_Pr1986765409at_nat,sK123,X2))) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_240])]) ).
thf(f2544,plain,
! [X2: set_Pr1986765409at_nat > nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,nat,X2,X0)),vAPP(set_Pr1986765409at_nat,nat,X2,X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,nat,X2,vAPP(sTfun(set_Pr1986765409at_nat,nat),set_Pr1986765409at_nat,sK122,X2))),vAPP(set_Pr1986765409at_nat,nat,X2,vAPP(sTfun(set_Pr1986765409at_nat,nat),set_Pr1986765409at_nat,sK123,X2))) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X1) ) ),
inference(equality_resolution,[],[f2446]) ).
thf(f2446,plain,
! [X2: set_Pr1986765409at_nat > nat,X3: nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,nat,X2,X0)),X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,nat,X2,vAPP(sTfun(set_Pr1986765409at_nat,nat),set_Pr1986765409at_nat,sK122,X2))),vAPP(set_Pr1986765409at_nat,nat,X2,vAPP(sTfun(set_Pr1986765409at_nat,nat),set_Pr1986765409at_nat,sK123,X2))) )
| ( vAPP(set_Pr1986765409at_nat,nat,X2,X1) != X3 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X1) ) ),
inference(definition_unfolding,[],[f2043,f1646,f1646,f1656]) ).
thf(f2043,plain,
! [X2: set_Pr1986765409at_nat > nat,X3: nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,X2,X0)),X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,X2,vAPP(sTfun(set_Pr1986765409at_nat,nat),set_Pr1986765409at_nat,sK122,X2))),vAPP(set_Pr1986765409at_nat,nat,X2,vAPP(sTfun(set_Pr1986765409at_nat,nat),set_Pr1986765409at_nat,sK123,X2))) )
| ( vAPP(set_Pr1986765409at_nat,nat,X2,X1) != X3 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1582]) ).
thf(f1582,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat > nat,X3: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,X2,X0)),X3) )
| ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,X2,vAPP(sTfun(set_Pr1986765409at_nat,nat),set_Pr1986765409at_nat,sK122,X2))),vAPP(set_Pr1986765409at_nat,nat,X2,vAPP(sTfun(set_Pr1986765409at_nat,nat),set_Pr1986765409at_nat,sK123,X2))) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(sTfun(set_Pr1986765409at_nat,nat),set_Pr1986765409at_nat,sK122,X2)),vAPP(sTfun(set_Pr1986765409at_nat,nat),set_Pr1986765409at_nat,sK123,X2)) ) )
| ( vAPP(set_Pr1986765409at_nat,nat,X2,X1) != X3 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK122,sK123])],[f1376,f1581]) ).
thf(f1581,plain,
! [X2: set_Pr1986765409at_nat > nat] :
( ? [X4: set_Pr1986765409at_nat,X5: set_Pr1986765409at_nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,X2,X4)),vAPP(set_Pr1986765409at_nat,nat,X2,X5)) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X4),X5) ) )
=> ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,X2,vAPP(sTfun(set_Pr1986765409at_nat,nat),set_Pr1986765409at_nat,sK122,X2))),vAPP(set_Pr1986765409at_nat,nat,X2,vAPP(sTfun(set_Pr1986765409at_nat,nat),set_Pr1986765409at_nat,sK123,X2))) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(sTfun(set_Pr1986765409at_nat,nat),set_Pr1986765409at_nat,sK122,X2)),vAPP(sTfun(set_Pr1986765409at_nat,nat),set_Pr1986765409at_nat,sK123,X2)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1376,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat > nat,X3: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,X2,X0)),X3) )
| ? [X4: set_Pr1986765409at_nat,X5: set_Pr1986765409at_nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,X2,X4)),vAPP(set_Pr1986765409at_nat,nat,X2,X5)) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X4),X5) ) )
| ( vAPP(set_Pr1986765409at_nat,nat,X2,X1) != X3 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1) ) ),
inference(flattening,[],[f1375]) ).
thf(f1375,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat > nat,X3: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,X2,X0)),X3) )
| ? [X4: set_Pr1986765409at_nat,X5: set_Pr1986765409at_nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,X2,X4)),vAPP(set_Pr1986765409at_nat,nat,X2,X5)) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X4),X5) ) )
| ( vAPP(set_Pr1986765409at_nat,nat,X2,X1) != X3 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1) ) ),
inference(ennf_transformation,[],[f957]) ).
thf(f957,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat > nat,X3: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1) )
=> ( ( vAPP(set_Pr1986765409at_nat,nat,X2,X1) = X3 )
=> ( ! [X4: set_Pr1986765409at_nat,X5: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X4),X5) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,X2,X4)),vAPP(set_Pr1986765409at_nat,nat,X2,X5)) ) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,X2,X0)),X3) ) ) ) ),
inference(fool_elimination,[],[f956]) ).
thf(f956,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat > nat,X3: nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1)
=> ( ( vAPP(set_Pr1986765409at_nat,nat,X2,X1) = X3 )
=> ( ! [X4: set_Pr1986765409at_nat,X5: set_Pr1986765409at_nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X4),X5)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,X2,X4)),vAPP(set_Pr1986765409at_nat,nat,X2,X5)) )
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,X2,X0)),X3) ) ) ),
inference(rectify,[],[f77]) ).
thf(f77,axiom,
! [X13: set_Pr1986765409at_nat,X12: set_Pr1986765409at_nat,X25: set_Pr1986765409at_nat > nat,X9: nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X13),X12)
=> ( ( vAPP(set_Pr1986765409at_nat,nat,X25,X12) = X9 )
=> ( ! [X4: set_Pr1986765409at_nat,X26: set_Pr1986765409at_nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X4),X26)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,X25,X4)),vAPP(set_Pr1986765409at_nat,nat,X25,X26)) )
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,X25,X13)),X9) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_ord__le__eq__subst) ).
thf(f6012,plain,
spl155_239,
inference(avatar_split_clause,[],[f2542,f6010]) ).
thf(f6010,plain,
( spl155_239
<=> ! [X2: set_Pr1986765409at_nat > set_nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_nat,X2,X0)),vAPP(set_Pr1986765409at_nat,set_nat,X2,X1)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_nat,X2,vAPP(sTfun(set_Pr1986765409at_nat,set_nat),set_Pr1986765409at_nat,sK120,X2))),vAPP(set_Pr1986765409at_nat,set_nat,X2,vAPP(sTfun(set_Pr1986765409at_nat,set_nat),set_Pr1986765409at_nat,sK121,X2))) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_239])]) ).
thf(f2542,plain,
! [X2: set_Pr1986765409at_nat > set_nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_nat,X2,X0)),vAPP(set_Pr1986765409at_nat,set_nat,X2,X1)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_nat,X2,vAPP(sTfun(set_Pr1986765409at_nat,set_nat),set_Pr1986765409at_nat,sK120,X2))),vAPP(set_Pr1986765409at_nat,set_nat,X2,vAPP(sTfun(set_Pr1986765409at_nat,set_nat),set_Pr1986765409at_nat,sK121,X2))) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X1) ) ),
inference(equality_resolution,[],[f2444]) ).
thf(f2444,plain,
! [X2: set_Pr1986765409at_nat > set_nat,X3: set_nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_nat,X2,X0)),X3) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_nat,X2,vAPP(sTfun(set_Pr1986765409at_nat,set_nat),set_Pr1986765409at_nat,sK120,X2))),vAPP(set_Pr1986765409at_nat,set_nat,X2,vAPP(sTfun(set_Pr1986765409at_nat,set_nat),set_Pr1986765409at_nat,sK121,X2))) )
| ( vAPP(set_Pr1986765409at_nat,set_nat,X2,X1) != X3 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X1) ) ),
inference(definition_unfolding,[],[f2041,f1650,f1650,f1656]) ).
thf(f2041,plain,
! [X2: set_Pr1986765409at_nat > set_nat,X3: set_nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_Pr1986765409at_nat,set_nat,X2,X0)),X3) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_Pr1986765409at_nat,set_nat,X2,vAPP(sTfun(set_Pr1986765409at_nat,set_nat),set_Pr1986765409at_nat,sK120,X2))),vAPP(set_Pr1986765409at_nat,set_nat,X2,vAPP(sTfun(set_Pr1986765409at_nat,set_nat),set_Pr1986765409at_nat,sK121,X2))) )
| ( vAPP(set_Pr1986765409at_nat,set_nat,X2,X1) != X3 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1580]) ).
thf(f1580,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat > set_nat,X3: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_Pr1986765409at_nat,set_nat,X2,X0)),X3) )
| ( ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_Pr1986765409at_nat,set_nat,X2,vAPP(sTfun(set_Pr1986765409at_nat,set_nat),set_Pr1986765409at_nat,sK120,X2))),vAPP(set_Pr1986765409at_nat,set_nat,X2,vAPP(sTfun(set_Pr1986765409at_nat,set_nat),set_Pr1986765409at_nat,sK121,X2))) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(sTfun(set_Pr1986765409at_nat,set_nat),set_Pr1986765409at_nat,sK120,X2)),vAPP(sTfun(set_Pr1986765409at_nat,set_nat),set_Pr1986765409at_nat,sK121,X2)) ) )
| ( vAPP(set_Pr1986765409at_nat,set_nat,X2,X1) != X3 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK120,sK121])],[f1374,f1579]) ).
thf(f1579,plain,
! [X2: set_Pr1986765409at_nat > set_nat] :
( ? [X4: set_Pr1986765409at_nat,X5: set_Pr1986765409at_nat] :
( ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_Pr1986765409at_nat,set_nat,X2,X4)),vAPP(set_Pr1986765409at_nat,set_nat,X2,X5)) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X4),X5) ) )
=> ( ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_Pr1986765409at_nat,set_nat,X2,vAPP(sTfun(set_Pr1986765409at_nat,set_nat),set_Pr1986765409at_nat,sK120,X2))),vAPP(set_Pr1986765409at_nat,set_nat,X2,vAPP(sTfun(set_Pr1986765409at_nat,set_nat),set_Pr1986765409at_nat,sK121,X2))) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(sTfun(set_Pr1986765409at_nat,set_nat),set_Pr1986765409at_nat,sK120,X2)),vAPP(sTfun(set_Pr1986765409at_nat,set_nat),set_Pr1986765409at_nat,sK121,X2)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1374,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat > set_nat,X3: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_Pr1986765409at_nat,set_nat,X2,X0)),X3) )
| ? [X4: set_Pr1986765409at_nat,X5: set_Pr1986765409at_nat] :
( ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_Pr1986765409at_nat,set_nat,X2,X4)),vAPP(set_Pr1986765409at_nat,set_nat,X2,X5)) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X4),X5) ) )
| ( vAPP(set_Pr1986765409at_nat,set_nat,X2,X1) != X3 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1) ) ),
inference(flattening,[],[f1373]) ).
thf(f1373,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat > set_nat,X3: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_Pr1986765409at_nat,set_nat,X2,X0)),X3) )
| ? [X4: set_Pr1986765409at_nat,X5: set_Pr1986765409at_nat] :
( ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_Pr1986765409at_nat,set_nat,X2,X4)),vAPP(set_Pr1986765409at_nat,set_nat,X2,X5)) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X4),X5) ) )
| ( vAPP(set_Pr1986765409at_nat,set_nat,X2,X1) != X3 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1) ) ),
inference(ennf_transformation,[],[f955]) ).
thf(f955,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat > set_nat,X3: set_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1) )
=> ( ( vAPP(set_Pr1986765409at_nat,set_nat,X2,X1) = X3 )
=> ( ! [X4: set_Pr1986765409at_nat,X5: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X4),X5) )
=> ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_Pr1986765409at_nat,set_nat,X2,X4)),vAPP(set_Pr1986765409at_nat,set_nat,X2,X5)) ) )
=> ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_Pr1986765409at_nat,set_nat,X2,X0)),X3) ) ) ) ),
inference(fool_elimination,[],[f954]) ).
thf(f954,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat > set_nat,X3: set_nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1)
=> ( ( vAPP(set_Pr1986765409at_nat,set_nat,X2,X1) = X3 )
=> ( ! [X4: set_Pr1986765409at_nat,X5: set_Pr1986765409at_nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X4),X5)
=> vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_Pr1986765409at_nat,set_nat,X2,X4)),vAPP(set_Pr1986765409at_nat,set_nat,X2,X5)) )
=> vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_Pr1986765409at_nat,set_nat,X2,X0)),X3) ) ) ),
inference(rectify,[],[f76]) ).
thf(f76,axiom,
! [X13: set_Pr1986765409at_nat,X12: set_Pr1986765409at_nat,X25: set_Pr1986765409at_nat > set_nat,X9: set_nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X13),X12)
=> ( ( vAPP(set_Pr1986765409at_nat,set_nat,X25,X12) = X9 )
=> ( ! [X4: set_Pr1986765409at_nat,X26: set_Pr1986765409at_nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X4),X26)
=> vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_Pr1986765409at_nat,set_nat,X25,X4)),vAPP(set_Pr1986765409at_nat,set_nat,X25,X26)) )
=> vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_Pr1986765409at_nat,set_nat,X25,X13)),X9) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_ord__le__eq__subst) ).
thf(f6008,plain,
spl155_238,
inference(avatar_split_clause,[],[f2540,f6006]) ).
thf(f6006,plain,
( spl155_238
<=> ! [X2: nat > set_Pr1986765409at_nat,X0: nat,X1: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(nat,set_Pr1986765409at_nat,X2,X0)),vAPP(nat,set_Pr1986765409at_nat,X2,X1)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(nat,set_Pr1986765409at_nat,X2,vAPP(sTfun(nat,set_Pr1986765409at_nat),nat,sK112,X2))),vAPP(nat,set_Pr1986765409at_nat,X2,vAPP(sTfun(nat,set_Pr1986765409at_nat),nat,sK113,X2))) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_238])]) ).
thf(f2540,plain,
! [X2: nat > set_Pr1986765409at_nat,X0: nat,X1: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(nat,set_Pr1986765409at_nat,X2,X0)),vAPP(nat,set_Pr1986765409at_nat,X2,X1)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(nat,set_Pr1986765409at_nat,X2,vAPP(sTfun(nat,set_Pr1986765409at_nat),nat,sK112,X2))),vAPP(nat,set_Pr1986765409at_nat,X2,vAPP(sTfun(nat,set_Pr1986765409at_nat),nat,sK113,X2))) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),X1) ) ),
inference(equality_resolution,[],[f2435]) ).
thf(f2435,plain,
! [X2: nat > set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat,X0: nat,X1: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(nat,set_Pr1986765409at_nat,X2,X0)),X3) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(nat,set_Pr1986765409at_nat,X2,vAPP(sTfun(nat,set_Pr1986765409at_nat),nat,sK112,X2))),vAPP(nat,set_Pr1986765409at_nat,X2,vAPP(sTfun(nat,set_Pr1986765409at_nat),nat,sK113,X2))) )
| ( vAPP(nat,set_Pr1986765409at_nat,X2,X1) != X3 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),X1) ) ),
inference(definition_unfolding,[],[f2032,f1656,f1656,f1646]) ).
thf(f2032,plain,
! [X2: nat > set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat,X0: nat,X1: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(nat,set_Pr1986765409at_nat,X2,X0)),X3) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(nat,set_Pr1986765409at_nat,X2,vAPP(sTfun(nat,set_Pr1986765409at_nat),nat,sK112,X2))),vAPP(nat,set_Pr1986765409at_nat,X2,vAPP(sTfun(nat,set_Pr1986765409at_nat),nat,sK113,X2))) )
| ( vAPP(nat,set_Pr1986765409at_nat,X2,X1) != X3 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1572]) ).
thf(f1572,plain,
! [X0: nat,X1: nat,X2: nat > set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(nat,set_Pr1986765409at_nat,X2,X0)),X3) )
| ( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(nat,set_Pr1986765409at_nat,X2,vAPP(sTfun(nat,set_Pr1986765409at_nat),nat,sK112,X2))),vAPP(nat,set_Pr1986765409at_nat,X2,vAPP(sTfun(nat,set_Pr1986765409at_nat),nat,sK113,X2))) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,set_Pr1986765409at_nat),nat,sK112,X2)),vAPP(sTfun(nat,set_Pr1986765409at_nat),nat,sK113,X2)) ) )
| ( vAPP(nat,set_Pr1986765409at_nat,X2,X1) != X3 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK112,sK113])],[f1364,f1571]) ).
thf(f1571,plain,
! [X2: nat > set_Pr1986765409at_nat] :
( ? [X4: nat,X5: nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(nat,set_Pr1986765409at_nat,X2,X4)),vAPP(nat,set_Pr1986765409at_nat,X2,X5)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) ) )
=> ( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(nat,set_Pr1986765409at_nat,X2,vAPP(sTfun(nat,set_Pr1986765409at_nat),nat,sK112,X2))),vAPP(nat,set_Pr1986765409at_nat,X2,vAPP(sTfun(nat,set_Pr1986765409at_nat),nat,sK113,X2))) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,set_Pr1986765409at_nat),nat,sK112,X2)),vAPP(sTfun(nat,set_Pr1986765409at_nat),nat,sK113,X2)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1364,plain,
! [X0: nat,X1: nat,X2: nat > set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(nat,set_Pr1986765409at_nat,X2,X0)),X3) )
| ? [X4: nat,X5: nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(nat,set_Pr1986765409at_nat,X2,X4)),vAPP(nat,set_Pr1986765409at_nat,X2,X5)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) ) )
| ( vAPP(nat,set_Pr1986765409at_nat,X2,X1) != X3 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(flattening,[],[f1363]) ).
thf(f1363,plain,
! [X0: nat,X1: nat,X2: nat > set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(nat,set_Pr1986765409at_nat,X2,X0)),X3) )
| ? [X4: nat,X5: nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(nat,set_Pr1986765409at_nat,X2,X4)),vAPP(nat,set_Pr1986765409at_nat,X2,X5)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) ) )
| ( vAPP(nat,set_Pr1986765409at_nat,X2,X1) != X3 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(ennf_transformation,[],[f945]) ).
thf(f945,plain,
! [X0: nat,X1: nat,X2: nat > set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
=> ( ( vAPP(nat,set_Pr1986765409at_nat,X2,X1) = X3 )
=> ( ! [X4: nat,X5: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) )
=> ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(nat,set_Pr1986765409at_nat,X2,X4)),vAPP(nat,set_Pr1986765409at_nat,X2,X5)) ) )
=> ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(nat,set_Pr1986765409at_nat,X2,X0)),X3) ) ) ) ),
inference(fool_elimination,[],[f944]) ).
thf(f944,plain,
! [X0: nat,X1: nat,X2: nat > set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1)
=> ( ( vAPP(nat,set_Pr1986765409at_nat,X2,X1) = X3 )
=> ( ! [X4: nat,X5: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5)
=> vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(nat,set_Pr1986765409at_nat,X2,X4)),vAPP(nat,set_Pr1986765409at_nat,X2,X5)) )
=> vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(nat,set_Pr1986765409at_nat,X2,X0)),X3) ) ) ),
inference(rectify,[],[f81]) ).
thf(f81,axiom,
! [X13: nat,X12: nat,X25: nat > set_Pr1986765409at_nat,X9: set_Pr1986765409at_nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X13),X12)
=> ( ( vAPP(nat,set_Pr1986765409at_nat,X25,X12) = X9 )
=> ( ! [X4: nat,X26: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X26)
=> vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(nat,set_Pr1986765409at_nat,X25,X4)),vAPP(nat,set_Pr1986765409at_nat,X25,X26)) )
=> vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(nat,set_Pr1986765409at_nat,X25,X13)),X9) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_ord__le__eq__subst) ).
thf(f6004,plain,
spl155_237,
inference(avatar_split_clause,[],[f2538,f6002]) ).
thf(f6002,plain,
( spl155_237
<=> ! [X2: nat > nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(nat,nat,X2,X0)),vAPP(nat,nat,X2,X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(nat,nat,X2,vAPP(sTfun(nat,nat),nat,sK110,X2))),vAPP(nat,nat,X2,vAPP(sTfun(nat,nat),nat,sK111,X2))) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_237])]) ).
thf(f2538,plain,
! [X2: nat > nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(nat,nat,X2,X0)),vAPP(nat,nat,X2,X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(nat,nat,X2,vAPP(sTfun(nat,nat),nat,sK110,X2))),vAPP(nat,nat,X2,vAPP(sTfun(nat,nat),nat,sK111,X2))) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),X1) ) ),
inference(equality_resolution,[],[f2433]) ).
thf(f2433,plain,
! [X2: nat > nat,X3: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(nat,nat,X2,X0)),X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(nat,nat,X2,vAPP(sTfun(nat,nat),nat,sK110,X2))),vAPP(nat,nat,X2,vAPP(sTfun(nat,nat),nat,sK111,X2))) )
| ( vAPP(nat,nat,X2,X1) != X3 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),X1) ) ),
inference(definition_unfolding,[],[f2030,f1646,f1646,f1646]) ).
thf(f2030,plain,
! [X2: nat > nat,X3: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,X0)),X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,vAPP(sTfun(nat,nat),nat,sK110,X2))),vAPP(nat,nat,X2,vAPP(sTfun(nat,nat),nat,sK111,X2))) )
| ( vAPP(nat,nat,X2,X1) != X3 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1570]) ).
thf(f1570,plain,
! [X0: nat,X1: nat,X2: nat > nat,X3: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,X0)),X3) )
| ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,vAPP(sTfun(nat,nat),nat,sK110,X2))),vAPP(nat,nat,X2,vAPP(sTfun(nat,nat),nat,sK111,X2))) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,nat),nat,sK110,X2)),vAPP(sTfun(nat,nat),nat,sK111,X2)) ) )
| ( vAPP(nat,nat,X2,X1) != X3 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK110,sK111])],[f1362,f1569]) ).
thf(f1569,plain,
! [X2: nat > nat] :
( ? [X4: nat,X5: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,X4)),vAPP(nat,nat,X2,X5)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) ) )
=> ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,vAPP(sTfun(nat,nat),nat,sK110,X2))),vAPP(nat,nat,X2,vAPP(sTfun(nat,nat),nat,sK111,X2))) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,nat),nat,sK110,X2)),vAPP(sTfun(nat,nat),nat,sK111,X2)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1362,plain,
! [X0: nat,X1: nat,X2: nat > nat,X3: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,X0)),X3) )
| ? [X4: nat,X5: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,X4)),vAPP(nat,nat,X2,X5)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) ) )
| ( vAPP(nat,nat,X2,X1) != X3 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(flattening,[],[f1361]) ).
thf(f1361,plain,
! [X0: nat,X1: nat,X2: nat > nat,X3: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,X0)),X3) )
| ? [X4: nat,X5: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,X4)),vAPP(nat,nat,X2,X5)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) ) )
| ( vAPP(nat,nat,X2,X1) != X3 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(ennf_transformation,[],[f943]) ).
thf(f943,plain,
! [X0: nat,X1: nat,X2: nat > nat,X3: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
=> ( ( vAPP(nat,nat,X2,X1) = X3 )
=> ( ! [X4: nat,X5: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,X4)),vAPP(nat,nat,X2,X5)) ) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,X0)),X3) ) ) ) ),
inference(fool_elimination,[],[f942]) ).
thf(f942,plain,
! [X0: nat,X1: nat,X2: nat > nat,X3: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1)
=> ( ( vAPP(nat,nat,X2,X1) = X3 )
=> ( ! [X4: nat,X5: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,X4)),vAPP(nat,nat,X2,X5)) )
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,X0)),X3) ) ) ),
inference(rectify,[],[f83]) ).
thf(f83,axiom,
! [X13: nat,X12: nat,X25: nat > nat,X9: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X13),X12)
=> ( ( vAPP(nat,nat,X25,X12) = X9 )
=> ( ! [X4: nat,X26: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X26)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X25,X4)),vAPP(nat,nat,X25,X26)) )
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X25,X13)),X9) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_ord__le__eq__subst) ).
thf(f6000,plain,
spl155_236,
inference(avatar_split_clause,[],[f2536,f5998]) ).
thf(f5998,plain,
( spl155_236
<=> ! [X2: nat > set_nat,X0: nat,X1: nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(nat,set_nat,X2,X0)),vAPP(nat,set_nat,X2,X1)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(nat,set_nat,X2,vAPP(sTfun(nat,set_nat),nat,sK108,X2))),vAPP(nat,set_nat,X2,vAPP(sTfun(nat,set_nat),nat,sK109,X2))) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_236])]) ).
thf(f2536,plain,
! [X2: nat > set_nat,X0: nat,X1: nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(nat,set_nat,X2,X0)),vAPP(nat,set_nat,X2,X1)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(nat,set_nat,X2,vAPP(sTfun(nat,set_nat),nat,sK108,X2))),vAPP(nat,set_nat,X2,vAPP(sTfun(nat,set_nat),nat,sK109,X2))) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),X1) ) ),
inference(equality_resolution,[],[f2431]) ).
thf(f2431,plain,
! [X2: nat > set_nat,X3: set_nat,X0: nat,X1: nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(nat,set_nat,X2,X0)),X3) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(nat,set_nat,X2,vAPP(sTfun(nat,set_nat),nat,sK108,X2))),vAPP(nat,set_nat,X2,vAPP(sTfun(nat,set_nat),nat,sK109,X2))) )
| ( vAPP(nat,set_nat,X2,X1) != X3 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),X1) ) ),
inference(definition_unfolding,[],[f2028,f1650,f1650,f1646]) ).
thf(f2028,plain,
! [X2: nat > set_nat,X3: set_nat,X0: nat,X1: nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(nat,set_nat,X2,X0)),X3) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(nat,set_nat,X2,vAPP(sTfun(nat,set_nat),nat,sK108,X2))),vAPP(nat,set_nat,X2,vAPP(sTfun(nat,set_nat),nat,sK109,X2))) )
| ( vAPP(nat,set_nat,X2,X1) != X3 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1568]) ).
thf(f1568,plain,
! [X0: nat,X1: nat,X2: nat > set_nat,X3: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(nat,set_nat,X2,X0)),X3) )
| ( ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(nat,set_nat,X2,vAPP(sTfun(nat,set_nat),nat,sK108,X2))),vAPP(nat,set_nat,X2,vAPP(sTfun(nat,set_nat),nat,sK109,X2))) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,set_nat),nat,sK108,X2)),vAPP(sTfun(nat,set_nat),nat,sK109,X2)) ) )
| ( vAPP(nat,set_nat,X2,X1) != X3 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK108,sK109])],[f1360,f1567]) ).
thf(f1567,plain,
! [X2: nat > set_nat] :
( ? [X4: nat,X5: nat] :
( ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(nat,set_nat,X2,X4)),vAPP(nat,set_nat,X2,X5)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) ) )
=> ( ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(nat,set_nat,X2,vAPP(sTfun(nat,set_nat),nat,sK108,X2))),vAPP(nat,set_nat,X2,vAPP(sTfun(nat,set_nat),nat,sK109,X2))) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,set_nat),nat,sK108,X2)),vAPP(sTfun(nat,set_nat),nat,sK109,X2)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1360,plain,
! [X0: nat,X1: nat,X2: nat > set_nat,X3: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(nat,set_nat,X2,X0)),X3) )
| ? [X4: nat,X5: nat] :
( ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(nat,set_nat,X2,X4)),vAPP(nat,set_nat,X2,X5)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) ) )
| ( vAPP(nat,set_nat,X2,X1) != X3 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(flattening,[],[f1359]) ).
thf(f1359,plain,
! [X0: nat,X1: nat,X2: nat > set_nat,X3: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(nat,set_nat,X2,X0)),X3) )
| ? [X4: nat,X5: nat] :
( ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(nat,set_nat,X2,X4)),vAPP(nat,set_nat,X2,X5)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) ) )
| ( vAPP(nat,set_nat,X2,X1) != X3 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(ennf_transformation,[],[f941]) ).
thf(f941,plain,
! [X0: nat,X1: nat,X2: nat > set_nat,X3: set_nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
=> ( ( vAPP(nat,set_nat,X2,X1) = X3 )
=> ( ! [X4: nat,X5: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) )
=> ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(nat,set_nat,X2,X4)),vAPP(nat,set_nat,X2,X5)) ) )
=> ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(nat,set_nat,X2,X0)),X3) ) ) ) ),
inference(fool_elimination,[],[f940]) ).
thf(f940,plain,
! [X0: nat,X1: nat,X2: nat > set_nat,X3: set_nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1)
=> ( ( vAPP(nat,set_nat,X2,X1) = X3 )
=> ( ! [X4: nat,X5: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5)
=> vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(nat,set_nat,X2,X4)),vAPP(nat,set_nat,X2,X5)) )
=> vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(nat,set_nat,X2,X0)),X3) ) ) ),
inference(rectify,[],[f82]) ).
thf(f82,axiom,
! [X13: nat,X12: nat,X25: nat > set_nat,X9: set_nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X13),X12)
=> ( ( vAPP(nat,set_nat,X25,X12) = X9 )
=> ( ! [X4: nat,X26: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X26)
=> vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(nat,set_nat,X25,X4)),vAPP(nat,set_nat,X25,X26)) )
=> vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(nat,set_nat,X25,X13)),X9) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_ord__le__eq__subst) ).
thf(f5989,plain,
spl155_235,
inference(avatar_split_clause,[],[f2534,f5987]) ).
thf(f5987,plain,
( spl155_235
<=> ! [X2: set_nat > set_Pr1986765409at_nat,X0: set_nat,X1: set_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_nat,set_Pr1986765409at_nat,X2,X0)),vAPP(set_nat,set_Pr1986765409at_nat,X2,X1)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_nat,set_Pr1986765409at_nat,X2,vAPP(sTfun(set_nat,set_Pr1986765409at_nat),set_nat,sK99,X2))),vAPP(set_nat,set_Pr1986765409at_nat,X2,vAPP(sTfun(set_nat,set_Pr1986765409at_nat),set_nat,sK100,X2))) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_235])]) ).
thf(f2534,plain,
! [X2: set_nat > set_Pr1986765409at_nat,X0: set_nat,X1: set_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_nat,set_Pr1986765409at_nat,X2,X0)),vAPP(set_nat,set_Pr1986765409at_nat,X2,X1)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_nat,set_Pr1986765409at_nat,X2,vAPP(sTfun(set_nat,set_Pr1986765409at_nat),set_nat,sK99,X2))),vAPP(set_nat,set_Pr1986765409at_nat,X2,vAPP(sTfun(set_nat,set_Pr1986765409at_nat),set_nat,sK100,X2))) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),X1) ) ),
inference(equality_resolution,[],[f2418]) ).
thf(f2418,plain,
! [X2: set_nat > set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat,X0: set_nat,X1: set_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_nat,set_Pr1986765409at_nat,X2,X0)),X3) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_nat,set_Pr1986765409at_nat,X2,vAPP(sTfun(set_nat,set_Pr1986765409at_nat),set_nat,sK99,X2))),vAPP(set_nat,set_Pr1986765409at_nat,X2,vAPP(sTfun(set_nat,set_Pr1986765409at_nat),set_nat,sK100,X2))) )
| ( vAPP(set_nat,set_Pr1986765409at_nat,X2,X1) != X3 )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),X1) ) ),
inference(definition_unfolding,[],[f2015,f1656,f1656,f1650]) ).
thf(f2015,plain,
! [X2: set_nat > set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat,X0: set_nat,X1: set_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_nat,set_Pr1986765409at_nat,X2,X0)),X3) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_nat,set_Pr1986765409at_nat,X2,vAPP(sTfun(set_nat,set_Pr1986765409at_nat),set_nat,sK99,X2))),vAPP(set_nat,set_Pr1986765409at_nat,X2,vAPP(sTfun(set_nat,set_Pr1986765409at_nat),set_nat,sK100,X2))) )
| ( vAPP(set_nat,set_Pr1986765409at_nat,X2,X1) != X3 )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1558]) ).
thf(f1558,plain,
! [X0: set_nat,X1: set_nat,X2: set_nat > set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_nat,set_Pr1986765409at_nat,X2,X0)),X3) )
| ( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_nat,set_Pr1986765409at_nat,X2,vAPP(sTfun(set_nat,set_Pr1986765409at_nat),set_nat,sK99,X2))),vAPP(set_nat,set_Pr1986765409at_nat,X2,vAPP(sTfun(set_nat,set_Pr1986765409at_nat),set_nat,sK100,X2))) )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(sTfun(set_nat,set_Pr1986765409at_nat),set_nat,sK99,X2)),vAPP(sTfun(set_nat,set_Pr1986765409at_nat),set_nat,sK100,X2)) ) )
| ( vAPP(set_nat,set_Pr1986765409at_nat,X2,X1) != X3 )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK99,sK100])],[f1346,f1557]) ).
thf(f1557,plain,
! [X2: set_nat > set_Pr1986765409at_nat] :
( ? [X4: set_nat,X5: set_nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_nat,set_Pr1986765409at_nat,X2,X4)),vAPP(set_nat,set_Pr1986765409at_nat,X2,X5)) )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X4),X5) ) )
=> ( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_nat,set_Pr1986765409at_nat,X2,vAPP(sTfun(set_nat,set_Pr1986765409at_nat),set_nat,sK99,X2))),vAPP(set_nat,set_Pr1986765409at_nat,X2,vAPP(sTfun(set_nat,set_Pr1986765409at_nat),set_nat,sK100,X2))) )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(sTfun(set_nat,set_Pr1986765409at_nat),set_nat,sK99,X2)),vAPP(sTfun(set_nat,set_Pr1986765409at_nat),set_nat,sK100,X2)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1346,plain,
! [X0: set_nat,X1: set_nat,X2: set_nat > set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_nat,set_Pr1986765409at_nat,X2,X0)),X3) )
| ? [X4: set_nat,X5: set_nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_nat,set_Pr1986765409at_nat,X2,X4)),vAPP(set_nat,set_Pr1986765409at_nat,X2,X5)) )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X4),X5) ) )
| ( vAPP(set_nat,set_Pr1986765409at_nat,X2,X1) != X3 )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1) ) ),
inference(flattening,[],[f1345]) ).
thf(f1345,plain,
! [X0: set_nat,X1: set_nat,X2: set_nat > set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_nat,set_Pr1986765409at_nat,X2,X0)),X3) )
| ? [X4: set_nat,X5: set_nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_nat,set_Pr1986765409at_nat,X2,X4)),vAPP(set_nat,set_Pr1986765409at_nat,X2,X5)) )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X4),X5) ) )
| ( vAPP(set_nat,set_Pr1986765409at_nat,X2,X1) != X3 )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1) ) ),
inference(ennf_transformation,[],[f927]) ).
thf(f927,plain,
! [X0: set_nat,X1: set_nat,X2: set_nat > set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1) )
=> ( ( vAPP(set_nat,set_Pr1986765409at_nat,X2,X1) = X3 )
=> ( ! [X4: set_nat,X5: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X4),X5) )
=> ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_nat,set_Pr1986765409at_nat,X2,X4)),vAPP(set_nat,set_Pr1986765409at_nat,X2,X5)) ) )
=> ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_nat,set_Pr1986765409at_nat,X2,X0)),X3) ) ) ) ),
inference(fool_elimination,[],[f926]) ).
thf(f926,plain,
! [X0: set_nat,X1: set_nat,X2: set_nat > set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat] :
( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1)
=> ( ( vAPP(set_nat,set_Pr1986765409at_nat,X2,X1) = X3 )
=> ( ! [X4: set_nat,X5: set_nat] :
( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X4),X5)
=> vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_nat,set_Pr1986765409at_nat,X2,X4)),vAPP(set_nat,set_Pr1986765409at_nat,X2,X5)) )
=> vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_nat,set_Pr1986765409at_nat,X2,X0)),X3) ) ) ),
inference(rectify,[],[f78]) ).
thf(f78,axiom,
! [X13: set_nat,X12: set_nat,X25: set_nat > set_Pr1986765409at_nat,X9: set_Pr1986765409at_nat] :
( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X13),X12)
=> ( ( vAPP(set_nat,set_Pr1986765409at_nat,X25,X12) = X9 )
=> ( ! [X4: set_nat,X26: set_nat] :
( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X4),X26)
=> vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_nat,set_Pr1986765409at_nat,X25,X4)),vAPP(set_nat,set_Pr1986765409at_nat,X25,X26)) )
=> vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_nat,set_Pr1986765409at_nat,X25,X13)),X9) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_ord__le__eq__subst) ).
thf(f5985,plain,
spl155_234,
inference(avatar_split_clause,[],[f2532,f5983]) ).
thf(f5983,plain,
( spl155_234
<=> ! [X2: set_nat > nat,X0: set_nat,X1: set_nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_nat,nat,X2,X0)),vAPP(set_nat,nat,X2,X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_nat,nat,X2,vAPP(sTfun(set_nat,nat),set_nat,sK97,X2))),vAPP(set_nat,nat,X2,vAPP(sTfun(set_nat,nat),set_nat,sK98,X2))) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_234])]) ).
thf(f2532,plain,
! [X2: set_nat > nat,X0: set_nat,X1: set_nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_nat,nat,X2,X0)),vAPP(set_nat,nat,X2,X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_nat,nat,X2,vAPP(sTfun(set_nat,nat),set_nat,sK97,X2))),vAPP(set_nat,nat,X2,vAPP(sTfun(set_nat,nat),set_nat,sK98,X2))) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),X1) ) ),
inference(equality_resolution,[],[f2416]) ).
thf(f2416,plain,
! [X2: set_nat > nat,X3: nat,X0: set_nat,X1: set_nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_nat,nat,X2,X0)),X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_nat,nat,X2,vAPP(sTfun(set_nat,nat),set_nat,sK97,X2))),vAPP(set_nat,nat,X2,vAPP(sTfun(set_nat,nat),set_nat,sK98,X2))) )
| ( vAPP(set_nat,nat,X2,X1) != X3 )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),X1) ) ),
inference(definition_unfolding,[],[f2013,f1646,f1646,f1650]) ).
thf(f2013,plain,
! [X2: set_nat > nat,X3: nat,X0: set_nat,X1: set_nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,X2,X0)),X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,X2,vAPP(sTfun(set_nat,nat),set_nat,sK97,X2))),vAPP(set_nat,nat,X2,vAPP(sTfun(set_nat,nat),set_nat,sK98,X2))) )
| ( vAPP(set_nat,nat,X2,X1) != X3 )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1556]) ).
thf(f1556,plain,
! [X0: set_nat,X1: set_nat,X2: set_nat > nat,X3: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,X2,X0)),X3) )
| ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,X2,vAPP(sTfun(set_nat,nat),set_nat,sK97,X2))),vAPP(set_nat,nat,X2,vAPP(sTfun(set_nat,nat),set_nat,sK98,X2))) )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(sTfun(set_nat,nat),set_nat,sK97,X2)),vAPP(sTfun(set_nat,nat),set_nat,sK98,X2)) ) )
| ( vAPP(set_nat,nat,X2,X1) != X3 )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK97,sK98])],[f1344,f1555]) ).
thf(f1555,plain,
! [X2: set_nat > nat] :
( ? [X4: set_nat,X5: set_nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,X2,X4)),vAPP(set_nat,nat,X2,X5)) )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X4),X5) ) )
=> ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,X2,vAPP(sTfun(set_nat,nat),set_nat,sK97,X2))),vAPP(set_nat,nat,X2,vAPP(sTfun(set_nat,nat),set_nat,sK98,X2))) )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(sTfun(set_nat,nat),set_nat,sK97,X2)),vAPP(sTfun(set_nat,nat),set_nat,sK98,X2)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1344,plain,
! [X0: set_nat,X1: set_nat,X2: set_nat > nat,X3: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,X2,X0)),X3) )
| ? [X4: set_nat,X5: set_nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,X2,X4)),vAPP(set_nat,nat,X2,X5)) )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X4),X5) ) )
| ( vAPP(set_nat,nat,X2,X1) != X3 )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1) ) ),
inference(flattening,[],[f1343]) ).
thf(f1343,plain,
! [X0: set_nat,X1: set_nat,X2: set_nat > nat,X3: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,X2,X0)),X3) )
| ? [X4: set_nat,X5: set_nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,X2,X4)),vAPP(set_nat,nat,X2,X5)) )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X4),X5) ) )
| ( vAPP(set_nat,nat,X2,X1) != X3 )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1) ) ),
inference(ennf_transformation,[],[f925]) ).
thf(f925,plain,
! [X0: set_nat,X1: set_nat,X2: set_nat > nat,X3: nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1) )
=> ( ( vAPP(set_nat,nat,X2,X1) = X3 )
=> ( ! [X4: set_nat,X5: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X4),X5) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,X2,X4)),vAPP(set_nat,nat,X2,X5)) ) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,X2,X0)),X3) ) ) ) ),
inference(fool_elimination,[],[f924]) ).
thf(f924,plain,
! [X0: set_nat,X1: set_nat,X2: set_nat > nat,X3: nat] :
( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1)
=> ( ( vAPP(set_nat,nat,X2,X1) = X3 )
=> ( ! [X4: set_nat,X5: set_nat] :
( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X4),X5)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,X2,X4)),vAPP(set_nat,nat,X2,X5)) )
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,X2,X0)),X3) ) ) ),
inference(rectify,[],[f80]) ).
thf(f80,axiom,
! [X13: set_nat,X12: set_nat,X25: set_nat > nat,X9: nat] :
( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X13),X12)
=> ( ( vAPP(set_nat,nat,X25,X12) = X9 )
=> ( ! [X4: set_nat,X26: set_nat] :
( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X4),X26)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,X25,X4)),vAPP(set_nat,nat,X25,X26)) )
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,X25,X13)),X9) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_ord__le__eq__subst) ).
thf(f5981,plain,
spl155_233,
inference(avatar_split_clause,[],[f2530,f5979]) ).
thf(f5979,plain,
( spl155_233
<=> ! [X2: set_nat > set_nat,X0: set_nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_nat,set_nat,X2,X0)),vAPP(set_nat,set_nat,X2,X1)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_nat,set_nat,X2,vAPP(sTfun(set_nat,set_nat),set_nat,sK95,X2))),vAPP(set_nat,set_nat,X2,vAPP(sTfun(set_nat,set_nat),set_nat,sK96,X2))) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_233])]) ).
thf(f2530,plain,
! [X2: set_nat > set_nat,X0: set_nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_nat,set_nat,X2,X0)),vAPP(set_nat,set_nat,X2,X1)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_nat,set_nat,X2,vAPP(sTfun(set_nat,set_nat),set_nat,sK95,X2))),vAPP(set_nat,set_nat,X2,vAPP(sTfun(set_nat,set_nat),set_nat,sK96,X2))) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),X1) ) ),
inference(equality_resolution,[],[f2414]) ).
thf(f2414,plain,
! [X2: set_nat > set_nat,X3: set_nat,X0: set_nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_nat,set_nat,X2,X0)),X3) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_nat,set_nat,X2,vAPP(sTfun(set_nat,set_nat),set_nat,sK95,X2))),vAPP(set_nat,set_nat,X2,vAPP(sTfun(set_nat,set_nat),set_nat,sK96,X2))) )
| ( vAPP(set_nat,set_nat,X2,X1) != X3 )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),X1) ) ),
inference(definition_unfolding,[],[f2011,f1650,f1650,f1650]) ).
thf(f2011,plain,
! [X2: set_nat > set_nat,X3: set_nat,X0: set_nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,X2,X0)),X3) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,X2,vAPP(sTfun(set_nat,set_nat),set_nat,sK95,X2))),vAPP(set_nat,set_nat,X2,vAPP(sTfun(set_nat,set_nat),set_nat,sK96,X2))) )
| ( vAPP(set_nat,set_nat,X2,X1) != X3 )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1554]) ).
thf(f1554,plain,
! [X0: set_nat,X1: set_nat,X2: set_nat > set_nat,X3: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,X2,X0)),X3) )
| ( ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,X2,vAPP(sTfun(set_nat,set_nat),set_nat,sK95,X2))),vAPP(set_nat,set_nat,X2,vAPP(sTfun(set_nat,set_nat),set_nat,sK96,X2))) )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(sTfun(set_nat,set_nat),set_nat,sK95,X2)),vAPP(sTfun(set_nat,set_nat),set_nat,sK96,X2)) ) )
| ( vAPP(set_nat,set_nat,X2,X1) != X3 )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK95,sK96])],[f1342,f1553]) ).
thf(f1553,plain,
! [X2: set_nat > set_nat] :
( ? [X4: set_nat,X5: set_nat] :
( ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,X2,X4)),vAPP(set_nat,set_nat,X2,X5)) )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X4),X5) ) )
=> ( ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,X2,vAPP(sTfun(set_nat,set_nat),set_nat,sK95,X2))),vAPP(set_nat,set_nat,X2,vAPP(sTfun(set_nat,set_nat),set_nat,sK96,X2))) )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(sTfun(set_nat,set_nat),set_nat,sK95,X2)),vAPP(sTfun(set_nat,set_nat),set_nat,sK96,X2)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1342,plain,
! [X0: set_nat,X1: set_nat,X2: set_nat > set_nat,X3: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,X2,X0)),X3) )
| ? [X4: set_nat,X5: set_nat] :
( ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,X2,X4)),vAPP(set_nat,set_nat,X2,X5)) )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X4),X5) ) )
| ( vAPP(set_nat,set_nat,X2,X1) != X3 )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1) ) ),
inference(flattening,[],[f1341]) ).
thf(f1341,plain,
! [X0: set_nat,X1: set_nat,X2: set_nat > set_nat,X3: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,X2,X0)),X3) )
| ? [X4: set_nat,X5: set_nat] :
( ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,X2,X4)),vAPP(set_nat,set_nat,X2,X5)) )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X4),X5) ) )
| ( vAPP(set_nat,set_nat,X2,X1) != X3 )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1) ) ),
inference(ennf_transformation,[],[f923]) ).
thf(f923,plain,
! [X0: set_nat,X1: set_nat,X2: set_nat > set_nat,X3: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1) )
=> ( ( vAPP(set_nat,set_nat,X2,X1) = X3 )
=> ( ! [X4: set_nat,X5: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X4),X5) )
=> ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,X2,X4)),vAPP(set_nat,set_nat,X2,X5)) ) )
=> ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,X2,X0)),X3) ) ) ) ),
inference(fool_elimination,[],[f922]) ).
thf(f922,plain,
! [X0: set_nat,X1: set_nat,X2: set_nat > set_nat,X3: set_nat] :
( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1)
=> ( ( vAPP(set_nat,set_nat,X2,X1) = X3 )
=> ( ! [X4: set_nat,X5: set_nat] :
( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X4),X5)
=> vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,X2,X4)),vAPP(set_nat,set_nat,X2,X5)) )
=> vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,X2,X0)),X3) ) ) ),
inference(rectify,[],[f79]) ).
thf(f79,axiom,
! [X13: set_nat,X12: set_nat,X25: set_nat > set_nat,X9: set_nat] :
( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X13),X12)
=> ( ( vAPP(set_nat,set_nat,X25,X12) = X9 )
=> ( ! [X4: set_nat,X26: set_nat] :
( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X4),X26)
=> vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,X25,X4)),vAPP(set_nat,set_nat,X25,X26)) )
=> vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,X25,X13)),X9) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_ord__le__eq__subst) ).
thf(f5977,plain,
spl155_232,
inference(avatar_split_clause,[],[f2524,f5975]) ).
thf(f5975,plain,
( spl155_232
<=> ! [X2: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat > set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X1,X2)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X1,X3)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X1,vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),set_Pr1986765409at_nat,sK83,X1))),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X1,vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),set_Pr1986765409at_nat,sK84,X1))) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X2),X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_232])]) ).
thf(f2524,plain,
! [X2: set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat > set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X1,X2)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X1,X3)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X1,vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),set_Pr1986765409at_nat,sK83,X1))),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X1,vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),set_Pr1986765409at_nat,sK84,X1))) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X2),X3) ) ),
inference(equality_resolution,[],[f2412]) ).
thf(f2412,plain,
! [X2: set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat > set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X1,X3)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X1,vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),set_Pr1986765409at_nat,sK83,X1))),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X1,vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),set_Pr1986765409at_nat,sK84,X1))) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X2),X3) )
| ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X1,X2) != X0 ) ),
inference(definition_unfolding,[],[f2003,f1656,f1656,f1656]) ).
thf(f2003,plain,
! [X2: set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat > set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X1,X3)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X1,vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),set_Pr1986765409at_nat,sK83,X1))),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X1,vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),set_Pr1986765409at_nat,sK84,X1))) )
| ( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X2),X3) != $true )
| ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X1,X2) != X0 ) ),
inference(cnf_transformation,[],[f1546]) ).
thf(f1546,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat > set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X1,X3)) )
| ( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X1,vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),set_Pr1986765409at_nat,sK83,X1))),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X1,vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),set_Pr1986765409at_nat,sK84,X1))) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),set_Pr1986765409at_nat,sK83,X1)),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),set_Pr1986765409at_nat,sK84,X1)) ) )
| ( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X2),X3) != $true )
| ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X1,X2) != X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK83,sK84])],[f1336,f1545]) ).
thf(f1545,plain,
! [X1: set_Pr1986765409at_nat > set_Pr1986765409at_nat] :
( ? [X4: set_Pr1986765409at_nat,X5: set_Pr1986765409at_nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X1,X4)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X1,X5)) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X4),X5) ) )
=> ( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X1,vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),set_Pr1986765409at_nat,sK83,X1))),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X1,vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),set_Pr1986765409at_nat,sK84,X1))) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),set_Pr1986765409at_nat,sK83,X1)),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),set_Pr1986765409at_nat,sK84,X1)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1336,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat > set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X1,X3)) )
| ? [X4: set_Pr1986765409at_nat,X5: set_Pr1986765409at_nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X1,X4)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X1,X5)) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X4),X5) ) )
| ( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X2),X3) != $true )
| ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X1,X2) != X0 ) ),
inference(flattening,[],[f1335]) ).
thf(f1335,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat > set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X1,X3)) )
| ? [X4: set_Pr1986765409at_nat,X5: set_Pr1986765409at_nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X1,X4)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X1,X5)) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X4),X5) ) )
| ( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X2),X3) != $true )
| ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X1,X2) != X0 ) ),
inference(ennf_transformation,[],[f917]) ).
thf(f917,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat > set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat] :
( ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X1,X2) = X0 )
=> ( ( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X2),X3) = $true )
=> ( ! [X4: set_Pr1986765409at_nat,X5: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X4),X5) )
=> ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X1,X4)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X1,X5)) ) )
=> ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X1,X3)) ) ) ) ),
inference(fool_elimination,[],[f916]) ).
thf(f916,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat > set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat] :
( ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X1,X2) = X0 )
=> ( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X2),X3)
=> ( ! [X4: set_Pr1986765409at_nat,X5: set_Pr1986765409at_nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X4),X5)
=> vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X1,X4)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X1,X5)) )
=> vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X1,X3)) ) ) ),
inference(rectify,[],[f84]) ).
thf(f84,axiom,
! [X13: set_Pr1986765409at_nat,X25: set_Pr1986765409at_nat > set_Pr1986765409at_nat,X12: set_Pr1986765409at_nat,X9: set_Pr1986765409at_nat] :
( ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X25,X12) = X13 )
=> ( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X12),X9)
=> ( ! [X4: set_Pr1986765409at_nat,X26: set_Pr1986765409at_nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X4),X26)
=> vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X25,X4)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X25,X26)) )
=> vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X13),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X25,X9)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_ord__eq__le__subst) ).
thf(f5973,plain,
spl155_231,
inference(avatar_split_clause,[],[f2522,f5971]) ).
thf(f5971,plain,
( spl155_231
<=> ! [X2: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat > nat,X3: set_Pr1986765409at_nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,nat,X1,X2)),vAPP(set_Pr1986765409at_nat,nat,X1,X3)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,nat,X1,vAPP(sTfun(set_Pr1986765409at_nat,nat),set_Pr1986765409at_nat,sK81,X1))),vAPP(set_Pr1986765409at_nat,nat,X1,vAPP(sTfun(set_Pr1986765409at_nat,nat),set_Pr1986765409at_nat,sK82,X1))) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X2),X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_231])]) ).
thf(f2522,plain,
! [X2: set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat > nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,nat,X1,X2)),vAPP(set_Pr1986765409at_nat,nat,X1,X3)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,nat,X1,vAPP(sTfun(set_Pr1986765409at_nat,nat),set_Pr1986765409at_nat,sK81,X1))),vAPP(set_Pr1986765409at_nat,nat,X1,vAPP(sTfun(set_Pr1986765409at_nat,nat),set_Pr1986765409at_nat,sK82,X1))) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X2),X3) ) ),
inference(equality_resolution,[],[f2410]) ).
thf(f2410,plain,
! [X2: set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat,X0: nat,X1: set_Pr1986765409at_nat > nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),vAPP(set_Pr1986765409at_nat,nat,X1,X3)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,nat,X1,vAPP(sTfun(set_Pr1986765409at_nat,nat),set_Pr1986765409at_nat,sK81,X1))),vAPP(set_Pr1986765409at_nat,nat,X1,vAPP(sTfun(set_Pr1986765409at_nat,nat),set_Pr1986765409at_nat,sK82,X1))) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X2),X3) )
| ( vAPP(set_Pr1986765409at_nat,nat,X1,X2) != X0 ) ),
inference(definition_unfolding,[],[f2001,f1646,f1646,f1656]) ).
thf(f2001,plain,
! [X2: set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat,X0: nat,X1: set_Pr1986765409at_nat > nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(set_Pr1986765409at_nat,nat,X1,X3)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,X1,vAPP(sTfun(set_Pr1986765409at_nat,nat),set_Pr1986765409at_nat,sK81,X1))),vAPP(set_Pr1986765409at_nat,nat,X1,vAPP(sTfun(set_Pr1986765409at_nat,nat),set_Pr1986765409at_nat,sK82,X1))) )
| ( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X2),X3) != $true )
| ( vAPP(set_Pr1986765409at_nat,nat,X1,X2) != X0 ) ),
inference(cnf_transformation,[],[f1544]) ).
thf(f1544,plain,
! [X0: nat,X1: set_Pr1986765409at_nat > nat,X2: set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(set_Pr1986765409at_nat,nat,X1,X3)) )
| ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,X1,vAPP(sTfun(set_Pr1986765409at_nat,nat),set_Pr1986765409at_nat,sK81,X1))),vAPP(set_Pr1986765409at_nat,nat,X1,vAPP(sTfun(set_Pr1986765409at_nat,nat),set_Pr1986765409at_nat,sK82,X1))) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(sTfun(set_Pr1986765409at_nat,nat),set_Pr1986765409at_nat,sK81,X1)),vAPP(sTfun(set_Pr1986765409at_nat,nat),set_Pr1986765409at_nat,sK82,X1)) ) )
| ( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X2),X3) != $true )
| ( vAPP(set_Pr1986765409at_nat,nat,X1,X2) != X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK81,sK82])],[f1334,f1543]) ).
thf(f1543,plain,
! [X1: set_Pr1986765409at_nat > nat] :
( ? [X4: set_Pr1986765409at_nat,X5: set_Pr1986765409at_nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,X1,X4)),vAPP(set_Pr1986765409at_nat,nat,X1,X5)) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X4),X5) ) )
=> ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,X1,vAPP(sTfun(set_Pr1986765409at_nat,nat),set_Pr1986765409at_nat,sK81,X1))),vAPP(set_Pr1986765409at_nat,nat,X1,vAPP(sTfun(set_Pr1986765409at_nat,nat),set_Pr1986765409at_nat,sK82,X1))) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(sTfun(set_Pr1986765409at_nat,nat),set_Pr1986765409at_nat,sK81,X1)),vAPP(sTfun(set_Pr1986765409at_nat,nat),set_Pr1986765409at_nat,sK82,X1)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1334,plain,
! [X0: nat,X1: set_Pr1986765409at_nat > nat,X2: set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(set_Pr1986765409at_nat,nat,X1,X3)) )
| ? [X4: set_Pr1986765409at_nat,X5: set_Pr1986765409at_nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,X1,X4)),vAPP(set_Pr1986765409at_nat,nat,X1,X5)) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X4),X5) ) )
| ( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X2),X3) != $true )
| ( vAPP(set_Pr1986765409at_nat,nat,X1,X2) != X0 ) ),
inference(flattening,[],[f1333]) ).
thf(f1333,plain,
! [X0: nat,X1: set_Pr1986765409at_nat > nat,X2: set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(set_Pr1986765409at_nat,nat,X1,X3)) )
| ? [X4: set_Pr1986765409at_nat,X5: set_Pr1986765409at_nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,X1,X4)),vAPP(set_Pr1986765409at_nat,nat,X1,X5)) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X4),X5) ) )
| ( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X2),X3) != $true )
| ( vAPP(set_Pr1986765409at_nat,nat,X1,X2) != X0 ) ),
inference(ennf_transformation,[],[f915]) ).
thf(f915,plain,
! [X0: nat,X1: set_Pr1986765409at_nat > nat,X2: set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat] :
( ( vAPP(set_Pr1986765409at_nat,nat,X1,X2) = X0 )
=> ( ( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X2),X3) = $true )
=> ( ! [X4: set_Pr1986765409at_nat,X5: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X4),X5) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,X1,X4)),vAPP(set_Pr1986765409at_nat,nat,X1,X5)) ) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(set_Pr1986765409at_nat,nat,X1,X3)) ) ) ) ),
inference(fool_elimination,[],[f914]) ).
thf(f914,plain,
! [X0: nat,X1: set_Pr1986765409at_nat > nat,X2: set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat] :
( ( vAPP(set_Pr1986765409at_nat,nat,X1,X2) = X0 )
=> ( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X2),X3)
=> ( ! [X4: set_Pr1986765409at_nat,X5: set_Pr1986765409at_nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X4),X5)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,X1,X4)),vAPP(set_Pr1986765409at_nat,nat,X1,X5)) )
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(set_Pr1986765409at_nat,nat,X1,X3)) ) ) ),
inference(rectify,[],[f86]) ).
thf(f86,axiom,
! [X13: nat,X25: set_Pr1986765409at_nat > nat,X12: set_Pr1986765409at_nat,X9: set_Pr1986765409at_nat] :
( ( vAPP(set_Pr1986765409at_nat,nat,X25,X12) = X13 )
=> ( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X12),X9)
=> ( ! [X4: set_Pr1986765409at_nat,X26: set_Pr1986765409at_nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X4),X26)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,X25,X4)),vAPP(set_Pr1986765409at_nat,nat,X25,X26)) )
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X13),vAPP(set_Pr1986765409at_nat,nat,X25,X9)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_ord__eq__le__subst) ).
thf(f5969,plain,
spl155_230,
inference(avatar_split_clause,[],[f2520,f5967]) ).
thf(f5967,plain,
( spl155_230
<=> ! [X2: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat > set_nat,X3: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_nat,X1,X2)),vAPP(set_Pr1986765409at_nat,set_nat,X1,X3)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_nat,X1,vAPP(sTfun(set_Pr1986765409at_nat,set_nat),set_Pr1986765409at_nat,sK79,X1))),vAPP(set_Pr1986765409at_nat,set_nat,X1,vAPP(sTfun(set_Pr1986765409at_nat,set_nat),set_Pr1986765409at_nat,sK80,X1))) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X2),X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_230])]) ).
thf(f2520,plain,
! [X2: set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat > set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_nat,X1,X2)),vAPP(set_Pr1986765409at_nat,set_nat,X1,X3)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_nat,X1,vAPP(sTfun(set_Pr1986765409at_nat,set_nat),set_Pr1986765409at_nat,sK79,X1))),vAPP(set_Pr1986765409at_nat,set_nat,X1,vAPP(sTfun(set_Pr1986765409at_nat,set_nat),set_Pr1986765409at_nat,sK80,X1))) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X2),X3) ) ),
inference(equality_resolution,[],[f2408]) ).
thf(f2408,plain,
! [X2: set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat,X0: set_nat,X1: set_Pr1986765409at_nat > set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),vAPP(set_Pr1986765409at_nat,set_nat,X1,X3)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_nat,X1,vAPP(sTfun(set_Pr1986765409at_nat,set_nat),set_Pr1986765409at_nat,sK79,X1))),vAPP(set_Pr1986765409at_nat,set_nat,X1,vAPP(sTfun(set_Pr1986765409at_nat,set_nat),set_Pr1986765409at_nat,sK80,X1))) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X2),X3) )
| ( vAPP(set_Pr1986765409at_nat,set_nat,X1,X2) != X0 ) ),
inference(definition_unfolding,[],[f1999,f1650,f1650,f1656]) ).
thf(f1999,plain,
! [X2: set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat,X0: set_nat,X1: set_Pr1986765409at_nat > set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),vAPP(set_Pr1986765409at_nat,set_nat,X1,X3)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_Pr1986765409at_nat,set_nat,X1,vAPP(sTfun(set_Pr1986765409at_nat,set_nat),set_Pr1986765409at_nat,sK79,X1))),vAPP(set_Pr1986765409at_nat,set_nat,X1,vAPP(sTfun(set_Pr1986765409at_nat,set_nat),set_Pr1986765409at_nat,sK80,X1))) )
| ( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X2),X3) != $true )
| ( vAPP(set_Pr1986765409at_nat,set_nat,X1,X2) != X0 ) ),
inference(cnf_transformation,[],[f1542]) ).
thf(f1542,plain,
! [X0: set_nat,X1: set_Pr1986765409at_nat > set_nat,X2: set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),vAPP(set_Pr1986765409at_nat,set_nat,X1,X3)) )
| ( ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_Pr1986765409at_nat,set_nat,X1,vAPP(sTfun(set_Pr1986765409at_nat,set_nat),set_Pr1986765409at_nat,sK79,X1))),vAPP(set_Pr1986765409at_nat,set_nat,X1,vAPP(sTfun(set_Pr1986765409at_nat,set_nat),set_Pr1986765409at_nat,sK80,X1))) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(sTfun(set_Pr1986765409at_nat,set_nat),set_Pr1986765409at_nat,sK79,X1)),vAPP(sTfun(set_Pr1986765409at_nat,set_nat),set_Pr1986765409at_nat,sK80,X1)) ) )
| ( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X2),X3) != $true )
| ( vAPP(set_Pr1986765409at_nat,set_nat,X1,X2) != X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK79,sK80])],[f1332,f1541]) ).
thf(f1541,plain,
! [X1: set_Pr1986765409at_nat > set_nat] :
( ? [X4: set_Pr1986765409at_nat,X5: set_Pr1986765409at_nat] :
( ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_Pr1986765409at_nat,set_nat,X1,X4)),vAPP(set_Pr1986765409at_nat,set_nat,X1,X5)) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X4),X5) ) )
=> ( ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_Pr1986765409at_nat,set_nat,X1,vAPP(sTfun(set_Pr1986765409at_nat,set_nat),set_Pr1986765409at_nat,sK79,X1))),vAPP(set_Pr1986765409at_nat,set_nat,X1,vAPP(sTfun(set_Pr1986765409at_nat,set_nat),set_Pr1986765409at_nat,sK80,X1))) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(sTfun(set_Pr1986765409at_nat,set_nat),set_Pr1986765409at_nat,sK79,X1)),vAPP(sTfun(set_Pr1986765409at_nat,set_nat),set_Pr1986765409at_nat,sK80,X1)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1332,plain,
! [X0: set_nat,X1: set_Pr1986765409at_nat > set_nat,X2: set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),vAPP(set_Pr1986765409at_nat,set_nat,X1,X3)) )
| ? [X4: set_Pr1986765409at_nat,X5: set_Pr1986765409at_nat] :
( ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_Pr1986765409at_nat,set_nat,X1,X4)),vAPP(set_Pr1986765409at_nat,set_nat,X1,X5)) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X4),X5) ) )
| ( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X2),X3) != $true )
| ( vAPP(set_Pr1986765409at_nat,set_nat,X1,X2) != X0 ) ),
inference(flattening,[],[f1331]) ).
thf(f1331,plain,
! [X0: set_nat,X1: set_Pr1986765409at_nat > set_nat,X2: set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),vAPP(set_Pr1986765409at_nat,set_nat,X1,X3)) )
| ? [X4: set_Pr1986765409at_nat,X5: set_Pr1986765409at_nat] :
( ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_Pr1986765409at_nat,set_nat,X1,X4)),vAPP(set_Pr1986765409at_nat,set_nat,X1,X5)) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X4),X5) ) )
| ( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X2),X3) != $true )
| ( vAPP(set_Pr1986765409at_nat,set_nat,X1,X2) != X0 ) ),
inference(ennf_transformation,[],[f913]) ).
thf(f913,plain,
! [X0: set_nat,X1: set_Pr1986765409at_nat > set_nat,X2: set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat] :
( ( vAPP(set_Pr1986765409at_nat,set_nat,X1,X2) = X0 )
=> ( ( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X2),X3) = $true )
=> ( ! [X4: set_Pr1986765409at_nat,X5: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X4),X5) )
=> ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_Pr1986765409at_nat,set_nat,X1,X4)),vAPP(set_Pr1986765409at_nat,set_nat,X1,X5)) ) )
=> ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),vAPP(set_Pr1986765409at_nat,set_nat,X1,X3)) ) ) ) ),
inference(fool_elimination,[],[f912]) ).
thf(f912,plain,
! [X0: set_nat,X1: set_Pr1986765409at_nat > set_nat,X2: set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat] :
( ( vAPP(set_Pr1986765409at_nat,set_nat,X1,X2) = X0 )
=> ( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X2),X3)
=> ( ! [X4: set_Pr1986765409at_nat,X5: set_Pr1986765409at_nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X4),X5)
=> vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_Pr1986765409at_nat,set_nat,X1,X4)),vAPP(set_Pr1986765409at_nat,set_nat,X1,X5)) )
=> vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),vAPP(set_Pr1986765409at_nat,set_nat,X1,X3)) ) ) ),
inference(rectify,[],[f85]) ).
thf(f85,axiom,
! [X13: set_nat,X25: set_Pr1986765409at_nat > set_nat,X12: set_Pr1986765409at_nat,X9: set_Pr1986765409at_nat] :
( ( vAPP(set_Pr1986765409at_nat,set_nat,X25,X12) = X13 )
=> ( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X12),X9)
=> ( ! [X4: set_Pr1986765409at_nat,X26: set_Pr1986765409at_nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X4),X26)
=> vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_Pr1986765409at_nat,set_nat,X25,X4)),vAPP(set_Pr1986765409at_nat,set_nat,X25,X26)) )
=> vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X13),vAPP(set_Pr1986765409at_nat,set_nat,X25,X9)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_ord__eq__le__subst) ).
thf(f5965,plain,
spl155_229,
inference(avatar_split_clause,[],[f2518,f5963]) ).
thf(f5963,plain,
( spl155_229
<=> ! [X2: nat,X1: nat > set_Pr1986765409at_nat,X3: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(nat,set_Pr1986765409at_nat,X1,X2)),vAPP(nat,set_Pr1986765409at_nat,X1,X3)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(nat,set_Pr1986765409at_nat,X1,vAPP(sTfun(nat,set_Pr1986765409at_nat),nat,sK77,X1))),vAPP(nat,set_Pr1986765409at_nat,X1,vAPP(sTfun(nat,set_Pr1986765409at_nat),nat,sK78,X1))) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X2),X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_229])]) ).
thf(f2518,plain,
! [X2: nat,X3: nat,X1: nat > set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(nat,set_Pr1986765409at_nat,X1,X2)),vAPP(nat,set_Pr1986765409at_nat,X1,X3)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(nat,set_Pr1986765409at_nat,X1,vAPP(sTfun(nat,set_Pr1986765409at_nat),nat,sK77,X1))),vAPP(nat,set_Pr1986765409at_nat,X1,vAPP(sTfun(nat,set_Pr1986765409at_nat),nat,sK78,X1))) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X2),X3) ) ),
inference(equality_resolution,[],[f2406]) ).
thf(f2406,plain,
! [X2: nat,X3: nat,X0: set_Pr1986765409at_nat,X1: nat > set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),vAPP(nat,set_Pr1986765409at_nat,X1,X3)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(nat,set_Pr1986765409at_nat,X1,vAPP(sTfun(nat,set_Pr1986765409at_nat),nat,sK77,X1))),vAPP(nat,set_Pr1986765409at_nat,X1,vAPP(sTfun(nat,set_Pr1986765409at_nat),nat,sK78,X1))) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X2),X3) )
| ( vAPP(nat,set_Pr1986765409at_nat,X1,X2) != X0 ) ),
inference(definition_unfolding,[],[f1997,f1656,f1656,f1646]) ).
thf(f1997,plain,
! [X2: nat,X3: nat,X0: set_Pr1986765409at_nat,X1: nat > set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),vAPP(nat,set_Pr1986765409at_nat,X1,X3)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(nat,set_Pr1986765409at_nat,X1,vAPP(sTfun(nat,set_Pr1986765409at_nat),nat,sK77,X1))),vAPP(nat,set_Pr1986765409at_nat,X1,vAPP(sTfun(nat,set_Pr1986765409at_nat),nat,sK78,X1))) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
| ( vAPP(nat,set_Pr1986765409at_nat,X1,X2) != X0 ) ),
inference(cnf_transformation,[],[f1540]) ).
thf(f1540,plain,
! [X0: set_Pr1986765409at_nat,X1: nat > set_Pr1986765409at_nat,X2: nat,X3: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),vAPP(nat,set_Pr1986765409at_nat,X1,X3)) )
| ( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(nat,set_Pr1986765409at_nat,X1,vAPP(sTfun(nat,set_Pr1986765409at_nat),nat,sK77,X1))),vAPP(nat,set_Pr1986765409at_nat,X1,vAPP(sTfun(nat,set_Pr1986765409at_nat),nat,sK78,X1))) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,set_Pr1986765409at_nat),nat,sK77,X1)),vAPP(sTfun(nat,set_Pr1986765409at_nat),nat,sK78,X1)) ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
| ( vAPP(nat,set_Pr1986765409at_nat,X1,X2) != X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK77,sK78])],[f1330,f1539]) ).
thf(f1539,plain,
! [X1: nat > set_Pr1986765409at_nat] :
( ? [X4: nat,X5: nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(nat,set_Pr1986765409at_nat,X1,X4)),vAPP(nat,set_Pr1986765409at_nat,X1,X5)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) ) )
=> ( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(nat,set_Pr1986765409at_nat,X1,vAPP(sTfun(nat,set_Pr1986765409at_nat),nat,sK77,X1))),vAPP(nat,set_Pr1986765409at_nat,X1,vAPP(sTfun(nat,set_Pr1986765409at_nat),nat,sK78,X1))) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,set_Pr1986765409at_nat),nat,sK77,X1)),vAPP(sTfun(nat,set_Pr1986765409at_nat),nat,sK78,X1)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1330,plain,
! [X0: set_Pr1986765409at_nat,X1: nat > set_Pr1986765409at_nat,X2: nat,X3: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),vAPP(nat,set_Pr1986765409at_nat,X1,X3)) )
| ? [X4: nat,X5: nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(nat,set_Pr1986765409at_nat,X1,X4)),vAPP(nat,set_Pr1986765409at_nat,X1,X5)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
| ( vAPP(nat,set_Pr1986765409at_nat,X1,X2) != X0 ) ),
inference(flattening,[],[f1329]) ).
thf(f1329,plain,
! [X0: set_Pr1986765409at_nat,X1: nat > set_Pr1986765409at_nat,X2: nat,X3: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),vAPP(nat,set_Pr1986765409at_nat,X1,X3)) )
| ? [X4: nat,X5: nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(nat,set_Pr1986765409at_nat,X1,X4)),vAPP(nat,set_Pr1986765409at_nat,X1,X5)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
| ( vAPP(nat,set_Pr1986765409at_nat,X1,X2) != X0 ) ),
inference(ennf_transformation,[],[f911]) ).
thf(f911,plain,
! [X0: set_Pr1986765409at_nat,X1: nat > set_Pr1986765409at_nat,X2: nat,X3: nat] :
( ( vAPP(nat,set_Pr1986765409at_nat,X1,X2) = X0 )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
=> ( ! [X4: nat,X5: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) )
=> ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(nat,set_Pr1986765409at_nat,X1,X4)),vAPP(nat,set_Pr1986765409at_nat,X1,X5)) ) )
=> ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),vAPP(nat,set_Pr1986765409at_nat,X1,X3)) ) ) ) ),
inference(fool_elimination,[],[f910]) ).
thf(f910,plain,
! [X0: set_Pr1986765409at_nat,X1: nat > set_Pr1986765409at_nat,X2: nat,X3: nat] :
( ( vAPP(nat,set_Pr1986765409at_nat,X1,X2) = X0 )
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3)
=> ( ! [X4: nat,X5: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5)
=> vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(nat,set_Pr1986765409at_nat,X1,X4)),vAPP(nat,set_Pr1986765409at_nat,X1,X5)) )
=> vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),vAPP(nat,set_Pr1986765409at_nat,X1,X3)) ) ) ),
inference(rectify,[],[f90]) ).
thf(f90,axiom,
! [X13: set_Pr1986765409at_nat,X25: nat > set_Pr1986765409at_nat,X12: nat,X9: nat] :
( ( vAPP(nat,set_Pr1986765409at_nat,X25,X12) = X13 )
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X12),X9)
=> ( ! [X4: nat,X26: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X26)
=> vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(nat,set_Pr1986765409at_nat,X25,X4)),vAPP(nat,set_Pr1986765409at_nat,X25,X26)) )
=> vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X13),vAPP(nat,set_Pr1986765409at_nat,X25,X9)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_ord__eq__le__subst) ).
thf(f5961,plain,
spl155_228,
inference(avatar_split_clause,[],[f2516,f5959]) ).
thf(f5959,plain,
( spl155_228
<=> ! [X2: nat,X1: nat > nat,X3: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(nat,nat,X1,X2)),vAPP(nat,nat,X1,X3)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(nat,nat,X1,vAPP(sTfun(nat,nat),nat,sK75,X1))),vAPP(nat,nat,X1,vAPP(sTfun(nat,nat),nat,sK76,X1))) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X2),X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_228])]) ).
thf(f2516,plain,
! [X2: nat,X3: nat,X1: nat > nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(nat,nat,X1,X2)),vAPP(nat,nat,X1,X3)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(nat,nat,X1,vAPP(sTfun(nat,nat),nat,sK75,X1))),vAPP(nat,nat,X1,vAPP(sTfun(nat,nat),nat,sK76,X1))) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X2),X3) ) ),
inference(equality_resolution,[],[f2404]) ).
thf(f2404,plain,
! [X2: nat,X3: nat,X0: nat,X1: nat > nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),vAPP(nat,nat,X1,X3)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(nat,nat,X1,vAPP(sTfun(nat,nat),nat,sK75,X1))),vAPP(nat,nat,X1,vAPP(sTfun(nat,nat),nat,sK76,X1))) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X2),X3) )
| ( vAPP(nat,nat,X1,X2) != X0 ) ),
inference(definition_unfolding,[],[f1995,f1646,f1646,f1646]) ).
thf(f1995,plain,
! [X2: nat,X3: nat,X0: nat,X1: nat > nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,X1,X3)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X1,vAPP(sTfun(nat,nat),nat,sK75,X1))),vAPP(nat,nat,X1,vAPP(sTfun(nat,nat),nat,sK76,X1))) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
| ( vAPP(nat,nat,X1,X2) != X0 ) ),
inference(cnf_transformation,[],[f1538]) ).
thf(f1538,plain,
! [X0: nat,X1: nat > nat,X2: nat,X3: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,X1,X3)) )
| ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X1,vAPP(sTfun(nat,nat),nat,sK75,X1))),vAPP(nat,nat,X1,vAPP(sTfun(nat,nat),nat,sK76,X1))) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,nat),nat,sK75,X1)),vAPP(sTfun(nat,nat),nat,sK76,X1)) ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
| ( vAPP(nat,nat,X1,X2) != X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK75,sK76])],[f1328,f1537]) ).
thf(f1537,plain,
! [X1: nat > nat] :
( ? [X4: nat,X5: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X1,X4)),vAPP(nat,nat,X1,X5)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) ) )
=> ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X1,vAPP(sTfun(nat,nat),nat,sK75,X1))),vAPP(nat,nat,X1,vAPP(sTfun(nat,nat),nat,sK76,X1))) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,nat),nat,sK75,X1)),vAPP(sTfun(nat,nat),nat,sK76,X1)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1328,plain,
! [X0: nat,X1: nat > nat,X2: nat,X3: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,X1,X3)) )
| ? [X4: nat,X5: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X1,X4)),vAPP(nat,nat,X1,X5)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
| ( vAPP(nat,nat,X1,X2) != X0 ) ),
inference(flattening,[],[f1327]) ).
thf(f1327,plain,
! [X0: nat,X1: nat > nat,X2: nat,X3: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,X1,X3)) )
| ? [X4: nat,X5: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X1,X4)),vAPP(nat,nat,X1,X5)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
| ( vAPP(nat,nat,X1,X2) != X0 ) ),
inference(ennf_transformation,[],[f909]) ).
thf(f909,plain,
! [X0: nat,X1: nat > nat,X2: nat,X3: nat] :
( ( vAPP(nat,nat,X1,X2) = X0 )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
=> ( ! [X4: nat,X5: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X1,X4)),vAPP(nat,nat,X1,X5)) ) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,X1,X3)) ) ) ) ),
inference(fool_elimination,[],[f908]) ).
thf(f908,plain,
! [X0: nat,X1: nat > nat,X2: nat,X3: nat] :
( ( vAPP(nat,nat,X1,X2) = X0 )
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3)
=> ( ! [X4: nat,X5: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X1,X4)),vAPP(nat,nat,X1,X5)) )
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,X1,X3)) ) ) ),
inference(rectify,[],[f92]) ).
thf(f92,axiom,
! [X13: nat,X25: nat > nat,X12: nat,X9: nat] :
( ( vAPP(nat,nat,X25,X12) = X13 )
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X12),X9)
=> ( ! [X4: nat,X26: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X26)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X25,X4)),vAPP(nat,nat,X25,X26)) )
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X13),vAPP(nat,nat,X25,X9)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_ord__eq__le__subst) ).
thf(f5957,plain,
spl155_227,
inference(avatar_split_clause,[],[f2514,f5955]) ).
thf(f5955,plain,
( spl155_227
<=> ! [X2: nat,X1: nat > set_nat,X3: nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(nat,set_nat,X1,X2)),vAPP(nat,set_nat,X1,X3)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(nat,set_nat,X1,vAPP(sTfun(nat,set_nat),nat,sK73,X1))),vAPP(nat,set_nat,X1,vAPP(sTfun(nat,set_nat),nat,sK74,X1))) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X2),X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_227])]) ).
thf(f2514,plain,
! [X2: nat,X3: nat,X1: nat > set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(nat,set_nat,X1,X2)),vAPP(nat,set_nat,X1,X3)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(nat,set_nat,X1,vAPP(sTfun(nat,set_nat),nat,sK73,X1))),vAPP(nat,set_nat,X1,vAPP(sTfun(nat,set_nat),nat,sK74,X1))) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X2),X3) ) ),
inference(equality_resolution,[],[f2402]) ).
thf(f2402,plain,
! [X2: nat,X3: nat,X0: set_nat,X1: nat > set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),vAPP(nat,set_nat,X1,X3)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(nat,set_nat,X1,vAPP(sTfun(nat,set_nat),nat,sK73,X1))),vAPP(nat,set_nat,X1,vAPP(sTfun(nat,set_nat),nat,sK74,X1))) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X2),X3) )
| ( vAPP(nat,set_nat,X1,X2) != X0 ) ),
inference(definition_unfolding,[],[f1993,f1650,f1650,f1646]) ).
thf(f1993,plain,
! [X2: nat,X3: nat,X0: set_nat,X1: nat > set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),vAPP(nat,set_nat,X1,X3)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(nat,set_nat,X1,vAPP(sTfun(nat,set_nat),nat,sK73,X1))),vAPP(nat,set_nat,X1,vAPP(sTfun(nat,set_nat),nat,sK74,X1))) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
| ( vAPP(nat,set_nat,X1,X2) != X0 ) ),
inference(cnf_transformation,[],[f1536]) ).
thf(f1536,plain,
! [X0: set_nat,X1: nat > set_nat,X2: nat,X3: nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),vAPP(nat,set_nat,X1,X3)) )
| ( ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(nat,set_nat,X1,vAPP(sTfun(nat,set_nat),nat,sK73,X1))),vAPP(nat,set_nat,X1,vAPP(sTfun(nat,set_nat),nat,sK74,X1))) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,set_nat),nat,sK73,X1)),vAPP(sTfun(nat,set_nat),nat,sK74,X1)) ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
| ( vAPP(nat,set_nat,X1,X2) != X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK73,sK74])],[f1326,f1535]) ).
thf(f1535,plain,
! [X1: nat > set_nat] :
( ? [X4: nat,X5: nat] :
( ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(nat,set_nat,X1,X4)),vAPP(nat,set_nat,X1,X5)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) ) )
=> ( ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(nat,set_nat,X1,vAPP(sTfun(nat,set_nat),nat,sK73,X1))),vAPP(nat,set_nat,X1,vAPP(sTfun(nat,set_nat),nat,sK74,X1))) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,set_nat),nat,sK73,X1)),vAPP(sTfun(nat,set_nat),nat,sK74,X1)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1326,plain,
! [X0: set_nat,X1: nat > set_nat,X2: nat,X3: nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),vAPP(nat,set_nat,X1,X3)) )
| ? [X4: nat,X5: nat] :
( ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(nat,set_nat,X1,X4)),vAPP(nat,set_nat,X1,X5)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
| ( vAPP(nat,set_nat,X1,X2) != X0 ) ),
inference(flattening,[],[f1325]) ).
thf(f1325,plain,
! [X0: set_nat,X1: nat > set_nat,X2: nat,X3: nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),vAPP(nat,set_nat,X1,X3)) )
| ? [X4: nat,X5: nat] :
( ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(nat,set_nat,X1,X4)),vAPP(nat,set_nat,X1,X5)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
| ( vAPP(nat,set_nat,X1,X2) != X0 ) ),
inference(ennf_transformation,[],[f907]) ).
thf(f907,plain,
! [X0: set_nat,X1: nat > set_nat,X2: nat,X3: nat] :
( ( vAPP(nat,set_nat,X1,X2) = X0 )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
=> ( ! [X4: nat,X5: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) )
=> ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(nat,set_nat,X1,X4)),vAPP(nat,set_nat,X1,X5)) ) )
=> ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),vAPP(nat,set_nat,X1,X3)) ) ) ) ),
inference(fool_elimination,[],[f906]) ).
thf(f906,plain,
! [X0: set_nat,X1: nat > set_nat,X2: nat,X3: nat] :
( ( vAPP(nat,set_nat,X1,X2) = X0 )
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3)
=> ( ! [X4: nat,X5: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5)
=> vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(nat,set_nat,X1,X4)),vAPP(nat,set_nat,X1,X5)) )
=> vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),vAPP(nat,set_nat,X1,X3)) ) ) ),
inference(rectify,[],[f91]) ).
thf(f91,axiom,
! [X13: set_nat,X25: nat > set_nat,X12: nat,X9: nat] :
( ( vAPP(nat,set_nat,X25,X12) = X13 )
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X12),X9)
=> ( ! [X4: nat,X26: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X26)
=> vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(nat,set_nat,X25,X4)),vAPP(nat,set_nat,X25,X26)) )
=> vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X13),vAPP(nat,set_nat,X25,X9)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_ord__eq__le__subst) ).
thf(f5953,plain,
spl155_226,
inference(avatar_split_clause,[],[f2512,f5951]) ).
thf(f5951,plain,
( spl155_226
<=> ! [X2: set_nat,X1: set_nat > set_Pr1986765409at_nat,X3: set_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_nat,set_Pr1986765409at_nat,X1,X2)),vAPP(set_nat,set_Pr1986765409at_nat,X1,X3)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_nat,set_Pr1986765409at_nat,X1,vAPP(sTfun(set_nat,set_Pr1986765409at_nat),set_nat,sK71,X1))),vAPP(set_nat,set_Pr1986765409at_nat,X1,vAPP(sTfun(set_nat,set_Pr1986765409at_nat),set_nat,sK72,X1))) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X2),X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_226])]) ).
thf(f2512,plain,
! [X2: set_nat,X3: set_nat,X1: set_nat > set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_nat,set_Pr1986765409at_nat,X1,X2)),vAPP(set_nat,set_Pr1986765409at_nat,X1,X3)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_nat,set_Pr1986765409at_nat,X1,vAPP(sTfun(set_nat,set_Pr1986765409at_nat),set_nat,sK71,X1))),vAPP(set_nat,set_Pr1986765409at_nat,X1,vAPP(sTfun(set_nat,set_Pr1986765409at_nat),set_nat,sK72,X1))) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X2),X3) ) ),
inference(equality_resolution,[],[f2400]) ).
thf(f2400,plain,
! [X2: set_nat,X3: set_nat,X0: set_Pr1986765409at_nat,X1: set_nat > set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),vAPP(set_nat,set_Pr1986765409at_nat,X1,X3)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_nat,set_Pr1986765409at_nat,X1,vAPP(sTfun(set_nat,set_Pr1986765409at_nat),set_nat,sK71,X1))),vAPP(set_nat,set_Pr1986765409at_nat,X1,vAPP(sTfun(set_nat,set_Pr1986765409at_nat),set_nat,sK72,X1))) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X2),X3) )
| ( vAPP(set_nat,set_Pr1986765409at_nat,X1,X2) != X0 ) ),
inference(definition_unfolding,[],[f1991,f1656,f1656,f1650]) ).
thf(f1991,plain,
! [X2: set_nat,X3: set_nat,X0: set_Pr1986765409at_nat,X1: set_nat > set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),vAPP(set_nat,set_Pr1986765409at_nat,X1,X3)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_nat,set_Pr1986765409at_nat,X1,vAPP(sTfun(set_nat,set_Pr1986765409at_nat),set_nat,sK71,X1))),vAPP(set_nat,set_Pr1986765409at_nat,X1,vAPP(sTfun(set_nat,set_Pr1986765409at_nat),set_nat,sK72,X1))) )
| ( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X3) != $true )
| ( vAPP(set_nat,set_Pr1986765409at_nat,X1,X2) != X0 ) ),
inference(cnf_transformation,[],[f1534]) ).
thf(f1534,plain,
! [X0: set_Pr1986765409at_nat,X1: set_nat > set_Pr1986765409at_nat,X2: set_nat,X3: set_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),vAPP(set_nat,set_Pr1986765409at_nat,X1,X3)) )
| ( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_nat,set_Pr1986765409at_nat,X1,vAPP(sTfun(set_nat,set_Pr1986765409at_nat),set_nat,sK71,X1))),vAPP(set_nat,set_Pr1986765409at_nat,X1,vAPP(sTfun(set_nat,set_Pr1986765409at_nat),set_nat,sK72,X1))) )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(sTfun(set_nat,set_Pr1986765409at_nat),set_nat,sK71,X1)),vAPP(sTfun(set_nat,set_Pr1986765409at_nat),set_nat,sK72,X1)) ) )
| ( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X3) != $true )
| ( vAPP(set_nat,set_Pr1986765409at_nat,X1,X2) != X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK71,sK72])],[f1324,f1533]) ).
thf(f1533,plain,
! [X1: set_nat > set_Pr1986765409at_nat] :
( ? [X4: set_nat,X5: set_nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_nat,set_Pr1986765409at_nat,X1,X4)),vAPP(set_nat,set_Pr1986765409at_nat,X1,X5)) )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X4),X5) ) )
=> ( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_nat,set_Pr1986765409at_nat,X1,vAPP(sTfun(set_nat,set_Pr1986765409at_nat),set_nat,sK71,X1))),vAPP(set_nat,set_Pr1986765409at_nat,X1,vAPP(sTfun(set_nat,set_Pr1986765409at_nat),set_nat,sK72,X1))) )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(sTfun(set_nat,set_Pr1986765409at_nat),set_nat,sK71,X1)),vAPP(sTfun(set_nat,set_Pr1986765409at_nat),set_nat,sK72,X1)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1324,plain,
! [X0: set_Pr1986765409at_nat,X1: set_nat > set_Pr1986765409at_nat,X2: set_nat,X3: set_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),vAPP(set_nat,set_Pr1986765409at_nat,X1,X3)) )
| ? [X4: set_nat,X5: set_nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_nat,set_Pr1986765409at_nat,X1,X4)),vAPP(set_nat,set_Pr1986765409at_nat,X1,X5)) )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X4),X5) ) )
| ( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X3) != $true )
| ( vAPP(set_nat,set_Pr1986765409at_nat,X1,X2) != X0 ) ),
inference(flattening,[],[f1323]) ).
thf(f1323,plain,
! [X0: set_Pr1986765409at_nat,X1: set_nat > set_Pr1986765409at_nat,X2: set_nat,X3: set_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),vAPP(set_nat,set_Pr1986765409at_nat,X1,X3)) )
| ? [X4: set_nat,X5: set_nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_nat,set_Pr1986765409at_nat,X1,X4)),vAPP(set_nat,set_Pr1986765409at_nat,X1,X5)) )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X4),X5) ) )
| ( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X3) != $true )
| ( vAPP(set_nat,set_Pr1986765409at_nat,X1,X2) != X0 ) ),
inference(ennf_transformation,[],[f905]) ).
thf(f905,plain,
! [X0: set_Pr1986765409at_nat,X1: set_nat > set_Pr1986765409at_nat,X2: set_nat,X3: set_nat] :
( ( vAPP(set_nat,set_Pr1986765409at_nat,X1,X2) = X0 )
=> ( ( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X3) = $true )
=> ( ! [X4: set_nat,X5: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X4),X5) )
=> ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_nat,set_Pr1986765409at_nat,X1,X4)),vAPP(set_nat,set_Pr1986765409at_nat,X1,X5)) ) )
=> ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),vAPP(set_nat,set_Pr1986765409at_nat,X1,X3)) ) ) ) ),
inference(fool_elimination,[],[f904]) ).
thf(f904,plain,
! [X0: set_Pr1986765409at_nat,X1: set_nat > set_Pr1986765409at_nat,X2: set_nat,X3: set_nat] :
( ( vAPP(set_nat,set_Pr1986765409at_nat,X1,X2) = X0 )
=> ( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X3)
=> ( ! [X4: set_nat,X5: set_nat] :
( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X4),X5)
=> vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_nat,set_Pr1986765409at_nat,X1,X4)),vAPP(set_nat,set_Pr1986765409at_nat,X1,X5)) )
=> vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),vAPP(set_nat,set_Pr1986765409at_nat,X1,X3)) ) ) ),
inference(rectify,[],[f87]) ).
thf(f87,axiom,
! [X13: set_Pr1986765409at_nat,X25: set_nat > set_Pr1986765409at_nat,X12: set_nat,X9: set_nat] :
( ( vAPP(set_nat,set_Pr1986765409at_nat,X25,X12) = X13 )
=> ( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X12),X9)
=> ( ! [X4: set_nat,X26: set_nat] :
( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X4),X26)
=> vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_nat,set_Pr1986765409at_nat,X25,X4)),vAPP(set_nat,set_Pr1986765409at_nat,X25,X26)) )
=> vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X13),vAPP(set_nat,set_Pr1986765409at_nat,X25,X9)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_ord__eq__le__subst) ).
thf(f5949,plain,
( spl155_225
| ~ spl155_68
| ~ spl155_104 ),
inference(avatar_split_clause,[],[f3581,f3484,f3209,f5947]) ).
thf(f5947,plain,
( spl155_225
<=> ! [X0: set_Pr1986765409at_nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK28,X0),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_225])]) ).
thf(f3581,plain,
( ! [X0: set_Pr1986765409at_nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK28,X0),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0))) )
| ~ spl155_68
| ~ spl155_104 ),
inference(trivial_inequality_removal,[],[f3570]) ).
thf(f3570,plain,
( ! [X0: set_Pr1986765409at_nat] :
( ( $true != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK28,X0),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0))) ) )
| ~ spl155_68
| ~ spl155_104 ),
inference(superposition,[],[f3485,f3210]) ).
thf(f5945,plain,
spl155_224,
inference(avatar_split_clause,[],[f2510,f5943]) ).
thf(f5943,plain,
( spl155_224
<=> ! [X2: set_nat,X1: set_nat > nat,X3: set_nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_nat,nat,X1,X2)),vAPP(set_nat,nat,X1,X3)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_nat,nat,X1,vAPP(sTfun(set_nat,nat),set_nat,sK69,X1))),vAPP(set_nat,nat,X1,vAPP(sTfun(set_nat,nat),set_nat,sK70,X1))) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X2),X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_224])]) ).
thf(f2510,plain,
! [X2: set_nat,X3: set_nat,X1: set_nat > nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_nat,nat,X1,X2)),vAPP(set_nat,nat,X1,X3)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_nat,nat,X1,vAPP(sTfun(set_nat,nat),set_nat,sK69,X1))),vAPP(set_nat,nat,X1,vAPP(sTfun(set_nat,nat),set_nat,sK70,X1))) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X2),X3) ) ),
inference(equality_resolution,[],[f2398]) ).
thf(f2398,plain,
! [X2: set_nat,X3: set_nat,X0: nat,X1: set_nat > nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),vAPP(set_nat,nat,X1,X3)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_nat,nat,X1,vAPP(sTfun(set_nat,nat),set_nat,sK69,X1))),vAPP(set_nat,nat,X1,vAPP(sTfun(set_nat,nat),set_nat,sK70,X1))) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X2),X3) )
| ( vAPP(set_nat,nat,X1,X2) != X0 ) ),
inference(definition_unfolding,[],[f1989,f1646,f1646,f1650]) ).
thf(f1989,plain,
! [X2: set_nat,X3: set_nat,X0: nat,X1: set_nat > nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(set_nat,nat,X1,X3)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,X1,vAPP(sTfun(set_nat,nat),set_nat,sK69,X1))),vAPP(set_nat,nat,X1,vAPP(sTfun(set_nat,nat),set_nat,sK70,X1))) )
| ( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X3) != $true )
| ( vAPP(set_nat,nat,X1,X2) != X0 ) ),
inference(cnf_transformation,[],[f1532]) ).
thf(f1532,plain,
! [X0: nat,X1: set_nat > nat,X2: set_nat,X3: set_nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(set_nat,nat,X1,X3)) )
| ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,X1,vAPP(sTfun(set_nat,nat),set_nat,sK69,X1))),vAPP(set_nat,nat,X1,vAPP(sTfun(set_nat,nat),set_nat,sK70,X1))) )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(sTfun(set_nat,nat),set_nat,sK69,X1)),vAPP(sTfun(set_nat,nat),set_nat,sK70,X1)) ) )
| ( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X3) != $true )
| ( vAPP(set_nat,nat,X1,X2) != X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK69,sK70])],[f1322,f1531]) ).
thf(f1531,plain,
! [X1: set_nat > nat] :
( ? [X4: set_nat,X5: set_nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,X1,X4)),vAPP(set_nat,nat,X1,X5)) )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X4),X5) ) )
=> ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,X1,vAPP(sTfun(set_nat,nat),set_nat,sK69,X1))),vAPP(set_nat,nat,X1,vAPP(sTfun(set_nat,nat),set_nat,sK70,X1))) )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(sTfun(set_nat,nat),set_nat,sK69,X1)),vAPP(sTfun(set_nat,nat),set_nat,sK70,X1)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1322,plain,
! [X0: nat,X1: set_nat > nat,X2: set_nat,X3: set_nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(set_nat,nat,X1,X3)) )
| ? [X4: set_nat,X5: set_nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,X1,X4)),vAPP(set_nat,nat,X1,X5)) )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X4),X5) ) )
| ( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X3) != $true )
| ( vAPP(set_nat,nat,X1,X2) != X0 ) ),
inference(flattening,[],[f1321]) ).
thf(f1321,plain,
! [X0: nat,X1: set_nat > nat,X2: set_nat,X3: set_nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(set_nat,nat,X1,X3)) )
| ? [X4: set_nat,X5: set_nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,X1,X4)),vAPP(set_nat,nat,X1,X5)) )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X4),X5) ) )
| ( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X3) != $true )
| ( vAPP(set_nat,nat,X1,X2) != X0 ) ),
inference(ennf_transformation,[],[f903]) ).
thf(f903,plain,
! [X0: nat,X1: set_nat > nat,X2: set_nat,X3: set_nat] :
( ( vAPP(set_nat,nat,X1,X2) = X0 )
=> ( ( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X3) = $true )
=> ( ! [X4: set_nat,X5: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X4),X5) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,X1,X4)),vAPP(set_nat,nat,X1,X5)) ) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(set_nat,nat,X1,X3)) ) ) ) ),
inference(fool_elimination,[],[f902]) ).
thf(f902,plain,
! [X0: nat,X1: set_nat > nat,X2: set_nat,X3: set_nat] :
( ( vAPP(set_nat,nat,X1,X2) = X0 )
=> ( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X3)
=> ( ! [X4: set_nat,X5: set_nat] :
( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X4),X5)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,X1,X4)),vAPP(set_nat,nat,X1,X5)) )
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(set_nat,nat,X1,X3)) ) ) ),
inference(rectify,[],[f89]) ).
thf(f89,axiom,
! [X13: nat,X25: set_nat > nat,X12: set_nat,X9: set_nat] :
( ( vAPP(set_nat,nat,X25,X12) = X13 )
=> ( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X12),X9)
=> ( ! [X4: set_nat,X26: set_nat] :
( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X4),X26)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,X25,X4)),vAPP(set_nat,nat,X25,X26)) )
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X13),vAPP(set_nat,nat,X25,X9)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_ord__eq__le__subst) ).
thf(f5941,plain,
spl155_223,
inference(avatar_split_clause,[],[f2508,f5939]) ).
thf(f5939,plain,
( spl155_223
<=> ! [X2: set_nat,X1: set_nat > set_nat,X3: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_nat,set_nat,X1,X2)),vAPP(set_nat,set_nat,X1,X3)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_nat,set_nat,X1,vAPP(sTfun(set_nat,set_nat),set_nat,sK67,X1))),vAPP(set_nat,set_nat,X1,vAPP(sTfun(set_nat,set_nat),set_nat,sK68,X1))) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X2),X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_223])]) ).
thf(f2508,plain,
! [X2: set_nat,X3: set_nat,X1: set_nat > set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_nat,set_nat,X1,X2)),vAPP(set_nat,set_nat,X1,X3)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_nat,set_nat,X1,vAPP(sTfun(set_nat,set_nat),set_nat,sK67,X1))),vAPP(set_nat,set_nat,X1,vAPP(sTfun(set_nat,set_nat),set_nat,sK68,X1))) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X2),X3) ) ),
inference(equality_resolution,[],[f2396]) ).
thf(f2396,plain,
! [X2: set_nat,X3: set_nat,X0: set_nat,X1: set_nat > set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),vAPP(set_nat,set_nat,X1,X3)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_nat,set_nat,X1,vAPP(sTfun(set_nat,set_nat),set_nat,sK67,X1))),vAPP(set_nat,set_nat,X1,vAPP(sTfun(set_nat,set_nat),set_nat,sK68,X1))) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X2),X3) )
| ( vAPP(set_nat,set_nat,X1,X2) != X0 ) ),
inference(definition_unfolding,[],[f1987,f1650,f1650,f1650]) ).
thf(f1987,plain,
! [X2: set_nat,X3: set_nat,X0: set_nat,X1: set_nat > set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),vAPP(set_nat,set_nat,X1,X3)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,X1,vAPP(sTfun(set_nat,set_nat),set_nat,sK67,X1))),vAPP(set_nat,set_nat,X1,vAPP(sTfun(set_nat,set_nat),set_nat,sK68,X1))) )
| ( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X3) != $true )
| ( vAPP(set_nat,set_nat,X1,X2) != X0 ) ),
inference(cnf_transformation,[],[f1530]) ).
thf(f1530,plain,
! [X0: set_nat,X1: set_nat > set_nat,X2: set_nat,X3: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),vAPP(set_nat,set_nat,X1,X3)) )
| ( ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,X1,vAPP(sTfun(set_nat,set_nat),set_nat,sK67,X1))),vAPP(set_nat,set_nat,X1,vAPP(sTfun(set_nat,set_nat),set_nat,sK68,X1))) )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(sTfun(set_nat,set_nat),set_nat,sK67,X1)),vAPP(sTfun(set_nat,set_nat),set_nat,sK68,X1)) ) )
| ( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X3) != $true )
| ( vAPP(set_nat,set_nat,X1,X2) != X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK67,sK68])],[f1320,f1529]) ).
thf(f1529,plain,
! [X1: set_nat > set_nat] :
( ? [X4: set_nat,X5: set_nat] :
( ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,X1,X4)),vAPP(set_nat,set_nat,X1,X5)) )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X4),X5) ) )
=> ( ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,X1,vAPP(sTfun(set_nat,set_nat),set_nat,sK67,X1))),vAPP(set_nat,set_nat,X1,vAPP(sTfun(set_nat,set_nat),set_nat,sK68,X1))) )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(sTfun(set_nat,set_nat),set_nat,sK67,X1)),vAPP(sTfun(set_nat,set_nat),set_nat,sK68,X1)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1320,plain,
! [X0: set_nat,X1: set_nat > set_nat,X2: set_nat,X3: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),vAPP(set_nat,set_nat,X1,X3)) )
| ? [X4: set_nat,X5: set_nat] :
( ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,X1,X4)),vAPP(set_nat,set_nat,X1,X5)) )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X4),X5) ) )
| ( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X3) != $true )
| ( vAPP(set_nat,set_nat,X1,X2) != X0 ) ),
inference(flattening,[],[f1319]) ).
thf(f1319,plain,
! [X0: set_nat,X1: set_nat > set_nat,X2: set_nat,X3: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),vAPP(set_nat,set_nat,X1,X3)) )
| ? [X4: set_nat,X5: set_nat] :
( ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,X1,X4)),vAPP(set_nat,set_nat,X1,X5)) )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X4),X5) ) )
| ( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X3) != $true )
| ( vAPP(set_nat,set_nat,X1,X2) != X0 ) ),
inference(ennf_transformation,[],[f901]) ).
thf(f901,plain,
! [X0: set_nat,X1: set_nat > set_nat,X2: set_nat,X3: set_nat] :
( ( vAPP(set_nat,set_nat,X1,X2) = X0 )
=> ( ( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X3) = $true )
=> ( ! [X4: set_nat,X5: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X4),X5) )
=> ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,X1,X4)),vAPP(set_nat,set_nat,X1,X5)) ) )
=> ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),vAPP(set_nat,set_nat,X1,X3)) ) ) ) ),
inference(fool_elimination,[],[f900]) ).
thf(f900,plain,
! [X0: set_nat,X1: set_nat > set_nat,X2: set_nat,X3: set_nat] :
( ( vAPP(set_nat,set_nat,X1,X2) = X0 )
=> ( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X3)
=> ( ! [X4: set_nat,X5: set_nat] :
( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X4),X5)
=> vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,X1,X4)),vAPP(set_nat,set_nat,X1,X5)) )
=> vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),vAPP(set_nat,set_nat,X1,X3)) ) ) ),
inference(rectify,[],[f88]) ).
thf(f88,axiom,
! [X13: set_nat,X25: set_nat > set_nat,X12: set_nat,X9: set_nat] :
( ( vAPP(set_nat,set_nat,X25,X12) = X13 )
=> ( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X12),X9)
=> ( ! [X4: set_nat,X26: set_nat] :
( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X4),X26)
=> vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,X25,X4)),vAPP(set_nat,set_nat,X25,X26)) )
=> vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X13),vAPP(set_nat,set_nat,X25,X9)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_ord__eq__le__subst) ).
thf(f5937,plain,
spl155_222,
inference(avatar_split_clause,[],[f2124,f5934]) ).
thf(f5934,plain,
( spl155_222
<=> ( vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB) = vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o)),sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vAPP(sTfun(sTfun(product_prod_nat_nat,$o),$o),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o)),sTfun(set_Pr1986765409at_nat,$o)),bCOMB,vPI(product_prod_nat_nat))),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o))),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o)))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o)))),cCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(sTfun(product_prod_nat_nat,$o),sTfun(product_prod_nat_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o)))),vAPP(sTfun(sTfun(sTfun(product_prod_nat_nat,$o),sTfun(product_prod_nat_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o)))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(sTfun(product_prod_nat_nat,$o),sTfun(product_prod_nat_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,sTfun($o,$o))),sTfun(set_Pr1986765409at_nat,sTfun(sTfun(product_prod_nat_nat,$o),sTfun(product_prod_nat_nat,$o))),vAPP(sTfun(sTfun(product_prod_nat_nat,sTfun($o,$o)),sTfun(sTfun(product_prod_nat_nat,$o),sTfun(product_prod_nat_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,sTfun($o,$o))),sTfun(set_Pr1986765409at_nat,sTfun(sTfun(product_prod_nat_nat,$o),sTfun(product_prod_nat_nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,sTfun($o,$o))),vAPP(sTfun(sTfun(product_prod_nat_nat,$o),sTfun(product_prod_nat_nat,sTfun($o,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(product_prod_nat_nat,$o),sTfun(product_prod_nat_nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o)),cCOMB,member701585322at_nat))))),vAPP(sTfun(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o)),cCOMB,member701585322at_nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_222])]) ).
thf(f2124,plain,
vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB) = vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o)),sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vAPP(sTfun(sTfun(product_prod_nat_nat,$o),$o),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o)),sTfun(set_Pr1986765409at_nat,$o)),bCOMB,vPI(product_prod_nat_nat))),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o))),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o)))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o)))),cCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(sTfun(product_prod_nat_nat,$o),sTfun(product_prod_nat_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o)))),vAPP(sTfun(sTfun(sTfun(product_prod_nat_nat,$o),sTfun(product_prod_nat_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o)))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(sTfun(product_prod_nat_nat,$o),sTfun(product_prod_nat_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,sTfun($o,$o))),sTfun(set_Pr1986765409at_nat,sTfun(sTfun(product_prod_nat_nat,$o),sTfun(product_prod_nat_nat,$o))),vAPP(sTfun(sTfun(product_prod_nat_nat,sTfun($o,$o)),sTfun(sTfun(product_prod_nat_nat,$o),sTfun(product_prod_nat_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,sTfun($o,$o))),sTfun(set_Pr1986765409at_nat,sTfun(sTfun(product_prod_nat_nat,$o),sTfun(product_prod_nat_nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,sTfun($o,$o))),vAPP(sTfun(sTfun(product_prod_nat_nat,$o),sTfun(product_prod_nat_nat,sTfun($o,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(product_prod_nat_nat,$o),sTfun(product_prod_nat_nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o)),cCOMB,member701585322at_nat))))),vAPP(sTfun(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o)),cCOMB,member701585322at_nat))),
inference(definition_unfolding,[],[f1660,f1656]) ).
thf(f1660,plain,
ord_le841296385at_nat = vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o)),sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vAPP(sTfun(sTfun(product_prod_nat_nat,$o),$o),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o)),sTfun(set_Pr1986765409at_nat,$o)),bCOMB,vPI(product_prod_nat_nat))),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o))),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o)))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o)))),cCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(sTfun(product_prod_nat_nat,$o),sTfun(product_prod_nat_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o)))),vAPP(sTfun(sTfun(sTfun(product_prod_nat_nat,$o),sTfun(product_prod_nat_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o)))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(sTfun(product_prod_nat_nat,$o),sTfun(product_prod_nat_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,sTfun($o,$o))),sTfun(set_Pr1986765409at_nat,sTfun(sTfun(product_prod_nat_nat,$o),sTfun(product_prod_nat_nat,$o))),vAPP(sTfun(sTfun(product_prod_nat_nat,sTfun($o,$o)),sTfun(sTfun(product_prod_nat_nat,$o),sTfun(product_prod_nat_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,sTfun($o,$o))),sTfun(set_Pr1986765409at_nat,sTfun(sTfun(product_prod_nat_nat,$o),sTfun(product_prod_nat_nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,sTfun($o,$o))),vAPP(sTfun(sTfun(product_prod_nat_nat,$o),sTfun(product_prod_nat_nat,sTfun($o,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(product_prod_nat_nat,$o),sTfun(product_prod_nat_nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o)),cCOMB,member701585322at_nat))))),vAPP(sTfun(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o)),cCOMB,member701585322at_nat))),
inference(cnf_transformation,[],[f415]) ).
thf(f415,plain,
ord_le841296385at_nat = vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o)),sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vAPP(sTfun(sTfun(product_prod_nat_nat,$o),$o),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o)),sTfun(set_Pr1986765409at_nat,$o)),bCOMB,vPI(product_prod_nat_nat))),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o))),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o)))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o)))),cCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(sTfun(product_prod_nat_nat,$o),sTfun(product_prod_nat_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o)))),vAPP(sTfun(sTfun(sTfun(product_prod_nat_nat,$o),sTfun(product_prod_nat_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o)))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(sTfun(product_prod_nat_nat,$o),sTfun(product_prod_nat_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,sTfun($o,$o))),sTfun(set_Pr1986765409at_nat,sTfun(sTfun(product_prod_nat_nat,$o),sTfun(product_prod_nat_nat,$o))),vAPP(sTfun(sTfun(product_prod_nat_nat,sTfun($o,$o)),sTfun(sTfun(product_prod_nat_nat,$o),sTfun(product_prod_nat_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,sTfun($o,$o))),sTfun(set_Pr1986765409at_nat,sTfun(sTfun(product_prod_nat_nat,$o),sTfun(product_prod_nat_nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,sTfun($o,$o))),vAPP(sTfun(sTfun(product_prod_nat_nat,$o),sTfun(product_prod_nat_nat,sTfun($o,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(product_prod_nat_nat,$o),sTfun(product_prod_nat_nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o)),cCOMB,member701585322at_nat))))),vAPP(sTfun(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o)),cCOMB,member701585322at_nat))),
inference(fool_elimination,[],[f414]) ).
thf(f414,plain,
( ord_le841296385at_nat
= ( ^ [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
! [X2: product_prod_nat_nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X2),X0)
=> vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X2),X1) ) ) ),
inference(rectify,[],[f125]) ).
thf(f125,axiom,
( ord_le841296385at_nat
= ( ^ [X28: set_Pr1986765409at_nat,X29: set_Pr1986765409at_nat] :
! [X31: product_prod_nat_nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X31),X28)
=> vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X31),X29) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_subset__iff) ).
thf(f5932,plain,
spl155_221,
inference(avatar_split_clause,[],[f2119,f5929]) ).
thf(f5929,plain,
( spl155_221
<=> ( vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB) = vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(set_nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(set_nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_221])]) ).
thf(f2119,plain,
vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB) = vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(set_nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(set_nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))),
inference(definition_unfolding,[],[f1654,f1650]) ).
thf(f1654,plain,
ord_less_eq_set_nat = vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(set_nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(set_nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))),
inference(cnf_transformation,[],[f403]) ).
thf(f403,plain,
ord_less_eq_set_nat = vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(nat,$o))),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(set_nat,sTfun(nat,$o))),vAPP(sTfun(set_nat,sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(set_nat,sTfun(nat,$o)))),cCOMB,vAPP(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,$o)))),sTfun(sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(set_nat,sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,$o))))),bCOMB,bCOMB),vAPP(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(set_nat,sTfun(nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(nat,$o)),sTfun(set_nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))))),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat))),
inference(fool_elimination,[],[f402]) ).
thf(f402,plain,
( ord_less_eq_set_nat
= ( ^ [X0: set_nat,X1: set_nat] :
! [X2: nat] :
( vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X2),X0)
=> vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X2),X1) ) ) ),
inference(rectify,[],[f126]) ).
thf(f126,axiom,
( ord_less_eq_set_nat
= ( ^ [X28: set_nat,X29: set_nat] :
! [X31: nat] :
( vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X31),X28)
=> vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X31),X29) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_subset__iff) ).
thf(f5463,plain,
spl155_220,
inference(avatar_split_clause,[],[f2547,f5461]) ).
thf(f5461,plain,
( spl155_220
<=> ! [X2: set_Pr1986765409at_nat > set_Pr1986765409at_nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X2,X0)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X2,X1)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),set_Pr1986765409at_nat,sK124,X2)),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),set_Pr1986765409at_nat,sK125,X2)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_220])]) ).
thf(f2547,plain,
! [X2: set_Pr1986765409at_nat > set_Pr1986765409at_nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X2,X0)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X2,X1)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),set_Pr1986765409at_nat,sK124,X2)),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),set_Pr1986765409at_nat,sK125,X2)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X1) ) ),
inference(equality_resolution,[],[f2449]) ).
thf(f2449,plain,
! [X2: set_Pr1986765409at_nat > set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X2,X0)),X3) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),set_Pr1986765409at_nat,sK124,X2)),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),set_Pr1986765409at_nat,sK125,X2)) )
| ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X2,X1) != X3 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X1) ) ),
inference(definition_unfolding,[],[f2044,f1656,f1656,f1656]) ).
thf(f2044,plain,
! [X2: set_Pr1986765409at_nat > set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X2,X0)),X3) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),set_Pr1986765409at_nat,sK124,X2)),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),set_Pr1986765409at_nat,sK125,X2)) )
| ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X2,X1) != X3 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1584]) ).
thf(f5459,plain,
spl155_219,
inference(avatar_split_clause,[],[f2545,f5457]) ).
thf(f5457,plain,
( spl155_219
<=> ! [X2: set_Pr1986765409at_nat > nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,nat,X2,X0)),vAPP(set_Pr1986765409at_nat,nat,X2,X1)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(sTfun(set_Pr1986765409at_nat,nat),set_Pr1986765409at_nat,sK122,X2)),vAPP(sTfun(set_Pr1986765409at_nat,nat),set_Pr1986765409at_nat,sK123,X2)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_219])]) ).
thf(f2545,plain,
! [X2: set_Pr1986765409at_nat > nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,nat,X2,X0)),vAPP(set_Pr1986765409at_nat,nat,X2,X1)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(sTfun(set_Pr1986765409at_nat,nat),set_Pr1986765409at_nat,sK122,X2)),vAPP(sTfun(set_Pr1986765409at_nat,nat),set_Pr1986765409at_nat,sK123,X2)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X1) ) ),
inference(equality_resolution,[],[f2447]) ).
thf(f2447,plain,
! [X2: set_Pr1986765409at_nat > nat,X3: nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,nat,X2,X0)),X3) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(sTfun(set_Pr1986765409at_nat,nat),set_Pr1986765409at_nat,sK122,X2)),vAPP(sTfun(set_Pr1986765409at_nat,nat),set_Pr1986765409at_nat,sK123,X2)) )
| ( vAPP(set_Pr1986765409at_nat,nat,X2,X1) != X3 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X1) ) ),
inference(definition_unfolding,[],[f2042,f1646,f1656,f1656]) ).
thf(f2042,plain,
! [X2: set_Pr1986765409at_nat > nat,X3: nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,X2,X0)),X3) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(sTfun(set_Pr1986765409at_nat,nat),set_Pr1986765409at_nat,sK122,X2)),vAPP(sTfun(set_Pr1986765409at_nat,nat),set_Pr1986765409at_nat,sK123,X2)) )
| ( vAPP(set_Pr1986765409at_nat,nat,X2,X1) != X3 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1582]) ).
thf(f5455,plain,
spl155_218,
inference(avatar_split_clause,[],[f2543,f5453]) ).
thf(f5453,plain,
( spl155_218
<=> ! [X2: set_Pr1986765409at_nat > set_nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_nat,X2,X0)),vAPP(set_Pr1986765409at_nat,set_nat,X2,X1)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(sTfun(set_Pr1986765409at_nat,set_nat),set_Pr1986765409at_nat,sK120,X2)),vAPP(sTfun(set_Pr1986765409at_nat,set_nat),set_Pr1986765409at_nat,sK121,X2)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_218])]) ).
thf(f2543,plain,
! [X2: set_Pr1986765409at_nat > set_nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_nat,X2,X0)),vAPP(set_Pr1986765409at_nat,set_nat,X2,X1)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(sTfun(set_Pr1986765409at_nat,set_nat),set_Pr1986765409at_nat,sK120,X2)),vAPP(sTfun(set_Pr1986765409at_nat,set_nat),set_Pr1986765409at_nat,sK121,X2)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X1) ) ),
inference(equality_resolution,[],[f2445]) ).
thf(f2445,plain,
! [X2: set_Pr1986765409at_nat > set_nat,X3: set_nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_nat,X2,X0)),X3) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(sTfun(set_Pr1986765409at_nat,set_nat),set_Pr1986765409at_nat,sK120,X2)),vAPP(sTfun(set_Pr1986765409at_nat,set_nat),set_Pr1986765409at_nat,sK121,X2)) )
| ( vAPP(set_Pr1986765409at_nat,set_nat,X2,X1) != X3 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X1) ) ),
inference(definition_unfolding,[],[f2040,f1650,f1656,f1656]) ).
thf(f2040,plain,
! [X2: set_Pr1986765409at_nat > set_nat,X3: set_nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_Pr1986765409at_nat,set_nat,X2,X0)),X3) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(sTfun(set_Pr1986765409at_nat,set_nat),set_Pr1986765409at_nat,sK120,X2)),vAPP(sTfun(set_Pr1986765409at_nat,set_nat),set_Pr1986765409at_nat,sK121,X2)) )
| ( vAPP(set_Pr1986765409at_nat,set_nat,X2,X1) != X3 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1580]) ).
thf(f5451,plain,
( spl155_217
| ~ spl155_11
| ~ spl155_154 ),
inference(avatar_split_clause,[],[f4461,f4321,f2814,f5449]) ).
thf(f5449,plain,
( spl155_217
<=> ! [X0: set_Pr1986765409at_nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),edges)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_217])]) ).
thf(f4321,plain,
( spl155_154
<=> ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,edges) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_154])]) ).
thf(f4461,plain,
( ! [X0: set_Pr1986765409at_nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),edges)) )
| ~ spl155_11
| ~ spl155_154 ),
inference(trivial_inequality_removal,[],[f4456]) ).
thf(f4456,plain,
( ! [X0: set_Pr1986765409at_nat] :
( ( $true != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),edges)) ) )
| ~ spl155_11
| ~ spl155_154 ),
inference(superposition,[],[f2815,f4323]) ).
thf(f4323,plain,
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,edges) )
| ~ spl155_154 ),
inference(avatar_component_clause,[],[f4321]) ).
thf(f5447,plain,
spl155_216,
inference(avatar_split_clause,[],[f2541,f5445]) ).
thf(f5445,plain,
( spl155_216
<=> ! [X2: nat > set_Pr1986765409at_nat,X0: nat,X1: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(nat,set_Pr1986765409at_nat,X2,X0)),vAPP(nat,set_Pr1986765409at_nat,X2,X1)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(sTfun(nat,set_Pr1986765409at_nat),nat,sK112,X2)),vAPP(sTfun(nat,set_Pr1986765409at_nat),nat,sK113,X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_216])]) ).
thf(f2541,plain,
! [X2: nat > set_Pr1986765409at_nat,X0: nat,X1: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(nat,set_Pr1986765409at_nat,X2,X0)),vAPP(nat,set_Pr1986765409at_nat,X2,X1)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(sTfun(nat,set_Pr1986765409at_nat),nat,sK112,X2)),vAPP(sTfun(nat,set_Pr1986765409at_nat),nat,sK113,X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),X1) ) ),
inference(equality_resolution,[],[f2436]) ).
thf(f2436,plain,
! [X2: nat > set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat,X0: nat,X1: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(nat,set_Pr1986765409at_nat,X2,X0)),X3) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(sTfun(nat,set_Pr1986765409at_nat),nat,sK112,X2)),vAPP(sTfun(nat,set_Pr1986765409at_nat),nat,sK113,X2)) )
| ( vAPP(nat,set_Pr1986765409at_nat,X2,X1) != X3 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),X1) ) ),
inference(definition_unfolding,[],[f2031,f1656,f1646,f1646]) ).
thf(f2031,plain,
! [X2: nat > set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat,X0: nat,X1: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(nat,set_Pr1986765409at_nat,X2,X0)),X3) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,set_Pr1986765409at_nat),nat,sK112,X2)),vAPP(sTfun(nat,set_Pr1986765409at_nat),nat,sK113,X2)) )
| ( vAPP(nat,set_Pr1986765409at_nat,X2,X1) != X3 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1572]) ).
thf(f5443,plain,
spl155_215,
inference(avatar_split_clause,[],[f2539,f5441]) ).
thf(f5441,plain,
( spl155_215
<=> ! [X2: nat > nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(nat,nat,X2,X0)),vAPP(nat,nat,X2,X1)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(sTfun(nat,nat),nat,sK110,X2)),vAPP(sTfun(nat,nat),nat,sK111,X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_215])]) ).
thf(f2539,plain,
! [X2: nat > nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(nat,nat,X2,X0)),vAPP(nat,nat,X2,X1)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(sTfun(nat,nat),nat,sK110,X2)),vAPP(sTfun(nat,nat),nat,sK111,X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),X1) ) ),
inference(equality_resolution,[],[f2434]) ).
thf(f2434,plain,
! [X2: nat > nat,X3: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(nat,nat,X2,X0)),X3) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(sTfun(nat,nat),nat,sK110,X2)),vAPP(sTfun(nat,nat),nat,sK111,X2)) )
| ( vAPP(nat,nat,X2,X1) != X3 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),X1) ) ),
inference(definition_unfolding,[],[f2029,f1646,f1646,f1646]) ).
thf(f2029,plain,
! [X2: nat > nat,X3: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,X0)),X3) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,nat),nat,sK110,X2)),vAPP(sTfun(nat,nat),nat,sK111,X2)) )
| ( vAPP(nat,nat,X2,X1) != X3 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1570]) ).
thf(f5439,plain,
spl155_214,
inference(avatar_split_clause,[],[f2537,f5437]) ).
thf(f5437,plain,
( spl155_214
<=> ! [X2: nat > set_nat,X0: nat,X1: nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(nat,set_nat,X2,X0)),vAPP(nat,set_nat,X2,X1)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(sTfun(nat,set_nat),nat,sK108,X2)),vAPP(sTfun(nat,set_nat),nat,sK109,X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_214])]) ).
thf(f2537,plain,
! [X2: nat > set_nat,X0: nat,X1: nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(nat,set_nat,X2,X0)),vAPP(nat,set_nat,X2,X1)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(sTfun(nat,set_nat),nat,sK108,X2)),vAPP(sTfun(nat,set_nat),nat,sK109,X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),X1) ) ),
inference(equality_resolution,[],[f2432]) ).
thf(f2432,plain,
! [X2: nat > set_nat,X3: set_nat,X0: nat,X1: nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(nat,set_nat,X2,X0)),X3) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(sTfun(nat,set_nat),nat,sK108,X2)),vAPP(sTfun(nat,set_nat),nat,sK109,X2)) )
| ( vAPP(nat,set_nat,X2,X1) != X3 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),X1) ) ),
inference(definition_unfolding,[],[f2027,f1650,f1646,f1646]) ).
thf(f2027,plain,
! [X2: nat > set_nat,X3: set_nat,X0: nat,X1: nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(nat,set_nat,X2,X0)),X3) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,set_nat),nat,sK108,X2)),vAPP(sTfun(nat,set_nat),nat,sK109,X2)) )
| ( vAPP(nat,set_nat,X2,X1) != X3 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1568]) ).
thf(f5435,plain,
spl155_213,
inference(avatar_split_clause,[],[f2535,f5433]) ).
thf(f5433,plain,
( spl155_213
<=> ! [X2: set_nat > set_Pr1986765409at_nat,X0: set_nat,X1: set_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_nat,set_Pr1986765409at_nat,X2,X0)),vAPP(set_nat,set_Pr1986765409at_nat,X2,X1)) )
| ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(sTfun(set_nat,set_Pr1986765409at_nat),set_nat,sK99,X2)),vAPP(sTfun(set_nat,set_Pr1986765409at_nat),set_nat,sK100,X2)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_213])]) ).
thf(f2535,plain,
! [X2: set_nat > set_Pr1986765409at_nat,X0: set_nat,X1: set_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_nat,set_Pr1986765409at_nat,X2,X0)),vAPP(set_nat,set_Pr1986765409at_nat,X2,X1)) )
| ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(sTfun(set_nat,set_Pr1986765409at_nat),set_nat,sK99,X2)),vAPP(sTfun(set_nat,set_Pr1986765409at_nat),set_nat,sK100,X2)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),X1) ) ),
inference(equality_resolution,[],[f2419]) ).
thf(f2419,plain,
! [X2: set_nat > set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat,X0: set_nat,X1: set_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_nat,set_Pr1986765409at_nat,X2,X0)),X3) )
| ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(sTfun(set_nat,set_Pr1986765409at_nat),set_nat,sK99,X2)),vAPP(sTfun(set_nat,set_Pr1986765409at_nat),set_nat,sK100,X2)) )
| ( vAPP(set_nat,set_Pr1986765409at_nat,X2,X1) != X3 )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),X1) ) ),
inference(definition_unfolding,[],[f2014,f1656,f1650,f1650]) ).
thf(f2014,plain,
! [X2: set_nat > set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat,X0: set_nat,X1: set_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_nat,set_Pr1986765409at_nat,X2,X0)),X3) )
| ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(sTfun(set_nat,set_Pr1986765409at_nat),set_nat,sK99,X2)),vAPP(sTfun(set_nat,set_Pr1986765409at_nat),set_nat,sK100,X2)) )
| ( vAPP(set_nat,set_Pr1986765409at_nat,X2,X1) != X3 )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1558]) ).
thf(f5431,plain,
spl155_212,
inference(avatar_split_clause,[],[f2533,f5429]) ).
thf(f5429,plain,
( spl155_212
<=> ! [X2: set_nat > nat,X0: set_nat,X1: set_nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_nat,nat,X2,X0)),vAPP(set_nat,nat,X2,X1)) )
| ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(sTfun(set_nat,nat),set_nat,sK97,X2)),vAPP(sTfun(set_nat,nat),set_nat,sK98,X2)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_212])]) ).
thf(f2533,plain,
! [X2: set_nat > nat,X0: set_nat,X1: set_nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_nat,nat,X2,X0)),vAPP(set_nat,nat,X2,X1)) )
| ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(sTfun(set_nat,nat),set_nat,sK97,X2)),vAPP(sTfun(set_nat,nat),set_nat,sK98,X2)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),X1) ) ),
inference(equality_resolution,[],[f2417]) ).
thf(f2417,plain,
! [X2: set_nat > nat,X3: nat,X0: set_nat,X1: set_nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_nat,nat,X2,X0)),X3) )
| ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(sTfun(set_nat,nat),set_nat,sK97,X2)),vAPP(sTfun(set_nat,nat),set_nat,sK98,X2)) )
| ( vAPP(set_nat,nat,X2,X1) != X3 )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),X1) ) ),
inference(definition_unfolding,[],[f2012,f1646,f1650,f1650]) ).
thf(f2012,plain,
! [X2: set_nat > nat,X3: nat,X0: set_nat,X1: set_nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,X2,X0)),X3) )
| ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(sTfun(set_nat,nat),set_nat,sK97,X2)),vAPP(sTfun(set_nat,nat),set_nat,sK98,X2)) )
| ( vAPP(set_nat,nat,X2,X1) != X3 )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1556]) ).
thf(f5427,plain,
spl155_211,
inference(avatar_split_clause,[],[f2531,f5425]) ).
thf(f5425,plain,
( spl155_211
<=> ! [X2: set_nat > set_nat,X0: set_nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_nat,set_nat,X2,X0)),vAPP(set_nat,set_nat,X2,X1)) )
| ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(sTfun(set_nat,set_nat),set_nat,sK95,X2)),vAPP(sTfun(set_nat,set_nat),set_nat,sK96,X2)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_211])]) ).
thf(f2531,plain,
! [X2: set_nat > set_nat,X0: set_nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_nat,set_nat,X2,X0)),vAPP(set_nat,set_nat,X2,X1)) )
| ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(sTfun(set_nat,set_nat),set_nat,sK95,X2)),vAPP(sTfun(set_nat,set_nat),set_nat,sK96,X2)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),X1) ) ),
inference(equality_resolution,[],[f2415]) ).
thf(f2415,plain,
! [X2: set_nat > set_nat,X3: set_nat,X0: set_nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_nat,set_nat,X2,X0)),X3) )
| ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(sTfun(set_nat,set_nat),set_nat,sK95,X2)),vAPP(sTfun(set_nat,set_nat),set_nat,sK96,X2)) )
| ( vAPP(set_nat,set_nat,X2,X1) != X3 )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),X1) ) ),
inference(definition_unfolding,[],[f2010,f1650,f1650,f1650]) ).
thf(f2010,plain,
! [X2: set_nat > set_nat,X3: set_nat,X0: set_nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,X2,X0)),X3) )
| ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(sTfun(set_nat,set_nat),set_nat,sK95,X2)),vAPP(sTfun(set_nat,set_nat),set_nat,sK96,X2)) )
| ( vAPP(set_nat,set_nat,X2,X1) != X3 )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1554]) ).
thf(f5423,plain,
spl155_210,
inference(avatar_split_clause,[],[f2525,f5421]) ).
thf(f5421,plain,
( spl155_210
<=> ! [X2: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat > set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X1,X2)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X1,X3)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),set_Pr1986765409at_nat,sK83,X1)),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),set_Pr1986765409at_nat,sK84,X1)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X2),X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_210])]) ).
thf(f2525,plain,
! [X2: set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat > set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X1,X2)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X1,X3)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),set_Pr1986765409at_nat,sK83,X1)),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),set_Pr1986765409at_nat,sK84,X1)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X2),X3) ) ),
inference(equality_resolution,[],[f2413]) ).
thf(f2413,plain,
! [X2: set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat > set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X1,X3)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),set_Pr1986765409at_nat,sK83,X1)),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),set_Pr1986765409at_nat,sK84,X1)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X2),X3) )
| ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X1,X2) != X0 ) ),
inference(definition_unfolding,[],[f2002,f1656,f1656,f1656]) ).
thf(f2002,plain,
! [X2: set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat > set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X1,X3)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),set_Pr1986765409at_nat,sK83,X1)),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),set_Pr1986765409at_nat,sK84,X1)) )
| ( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X2),X3) != $true )
| ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,X1,X2) != X0 ) ),
inference(cnf_transformation,[],[f1546]) ).
thf(f5419,plain,
spl155_209,
inference(avatar_split_clause,[],[f2523,f5417]) ).
thf(f5417,plain,
( spl155_209
<=> ! [X2: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat > nat,X3: set_Pr1986765409at_nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,nat,X1,X2)),vAPP(set_Pr1986765409at_nat,nat,X1,X3)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(sTfun(set_Pr1986765409at_nat,nat),set_Pr1986765409at_nat,sK81,X1)),vAPP(sTfun(set_Pr1986765409at_nat,nat),set_Pr1986765409at_nat,sK82,X1)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X2),X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_209])]) ).
thf(f2523,plain,
! [X2: set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat > nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,nat,X1,X2)),vAPP(set_Pr1986765409at_nat,nat,X1,X3)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(sTfun(set_Pr1986765409at_nat,nat),set_Pr1986765409at_nat,sK81,X1)),vAPP(sTfun(set_Pr1986765409at_nat,nat),set_Pr1986765409at_nat,sK82,X1)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X2),X3) ) ),
inference(equality_resolution,[],[f2411]) ).
thf(f2411,plain,
! [X2: set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat,X0: nat,X1: set_Pr1986765409at_nat > nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),vAPP(set_Pr1986765409at_nat,nat,X1,X3)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(sTfun(set_Pr1986765409at_nat,nat),set_Pr1986765409at_nat,sK81,X1)),vAPP(sTfun(set_Pr1986765409at_nat,nat),set_Pr1986765409at_nat,sK82,X1)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X2),X3) )
| ( vAPP(set_Pr1986765409at_nat,nat,X1,X2) != X0 ) ),
inference(definition_unfolding,[],[f2000,f1646,f1656,f1656]) ).
thf(f2000,plain,
! [X2: set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat,X0: nat,X1: set_Pr1986765409at_nat > nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(set_Pr1986765409at_nat,nat,X1,X3)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(sTfun(set_Pr1986765409at_nat,nat),set_Pr1986765409at_nat,sK81,X1)),vAPP(sTfun(set_Pr1986765409at_nat,nat),set_Pr1986765409at_nat,sK82,X1)) )
| ( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X2),X3) != $true )
| ( vAPP(set_Pr1986765409at_nat,nat,X1,X2) != X0 ) ),
inference(cnf_transformation,[],[f1544]) ).
thf(f5415,plain,
spl155_208,
inference(avatar_split_clause,[],[f2521,f5413]) ).
thf(f5413,plain,
( spl155_208
<=> ! [X2: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat > set_nat,X3: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_nat,X1,X2)),vAPP(set_Pr1986765409at_nat,set_nat,X1,X3)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(sTfun(set_Pr1986765409at_nat,set_nat),set_Pr1986765409at_nat,sK79,X1)),vAPP(sTfun(set_Pr1986765409at_nat,set_nat),set_Pr1986765409at_nat,sK80,X1)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X2),X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_208])]) ).
thf(f2521,plain,
! [X2: set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat > set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_nat,X1,X2)),vAPP(set_Pr1986765409at_nat,set_nat,X1,X3)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(sTfun(set_Pr1986765409at_nat,set_nat),set_Pr1986765409at_nat,sK79,X1)),vAPP(sTfun(set_Pr1986765409at_nat,set_nat),set_Pr1986765409at_nat,sK80,X1)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X2),X3) ) ),
inference(equality_resolution,[],[f2409]) ).
thf(f2409,plain,
! [X2: set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat,X0: set_nat,X1: set_Pr1986765409at_nat > set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),vAPP(set_Pr1986765409at_nat,set_nat,X1,X3)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(sTfun(set_Pr1986765409at_nat,set_nat),set_Pr1986765409at_nat,sK79,X1)),vAPP(sTfun(set_Pr1986765409at_nat,set_nat),set_Pr1986765409at_nat,sK80,X1)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X2),X3) )
| ( vAPP(set_Pr1986765409at_nat,set_nat,X1,X2) != X0 ) ),
inference(definition_unfolding,[],[f1998,f1650,f1656,f1656]) ).
thf(f1998,plain,
! [X2: set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat,X0: set_nat,X1: set_Pr1986765409at_nat > set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),vAPP(set_Pr1986765409at_nat,set_nat,X1,X3)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(sTfun(set_Pr1986765409at_nat,set_nat),set_Pr1986765409at_nat,sK79,X1)),vAPP(sTfun(set_Pr1986765409at_nat,set_nat),set_Pr1986765409at_nat,sK80,X1)) )
| ( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X2),X3) != $true )
| ( vAPP(set_Pr1986765409at_nat,set_nat,X1,X2) != X0 ) ),
inference(cnf_transformation,[],[f1542]) ).
thf(f5411,plain,
spl155_207,
inference(avatar_split_clause,[],[f2519,f5409]) ).
thf(f5409,plain,
( spl155_207
<=> ! [X2: nat,X1: nat > set_Pr1986765409at_nat,X3: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(nat,set_Pr1986765409at_nat,X1,X2)),vAPP(nat,set_Pr1986765409at_nat,X1,X3)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(sTfun(nat,set_Pr1986765409at_nat),nat,sK77,X1)),vAPP(sTfun(nat,set_Pr1986765409at_nat),nat,sK78,X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X2),X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_207])]) ).
thf(f2519,plain,
! [X2: nat,X3: nat,X1: nat > set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(nat,set_Pr1986765409at_nat,X1,X2)),vAPP(nat,set_Pr1986765409at_nat,X1,X3)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(sTfun(nat,set_Pr1986765409at_nat),nat,sK77,X1)),vAPP(sTfun(nat,set_Pr1986765409at_nat),nat,sK78,X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X2),X3) ) ),
inference(equality_resolution,[],[f2407]) ).
thf(f2407,plain,
! [X2: nat,X3: nat,X0: set_Pr1986765409at_nat,X1: nat > set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),vAPP(nat,set_Pr1986765409at_nat,X1,X3)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(sTfun(nat,set_Pr1986765409at_nat),nat,sK77,X1)),vAPP(sTfun(nat,set_Pr1986765409at_nat),nat,sK78,X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X2),X3) )
| ( vAPP(nat,set_Pr1986765409at_nat,X1,X2) != X0 ) ),
inference(definition_unfolding,[],[f1996,f1656,f1646,f1646]) ).
thf(f1996,plain,
! [X2: nat,X3: nat,X0: set_Pr1986765409at_nat,X1: nat > set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),vAPP(nat,set_Pr1986765409at_nat,X1,X3)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,set_Pr1986765409at_nat),nat,sK77,X1)),vAPP(sTfun(nat,set_Pr1986765409at_nat),nat,sK78,X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
| ( vAPP(nat,set_Pr1986765409at_nat,X1,X2) != X0 ) ),
inference(cnf_transformation,[],[f1540]) ).
thf(f5407,plain,
( spl155_206
| ~ spl155_10
| ~ spl155_154 ),
inference(avatar_split_clause,[],[f4460,f4321,f2810,f5405]) ).
thf(f5405,plain,
( spl155_206
<=> ! [X0: set_Pr1986765409at_nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,edges),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_206])]) ).
thf(f4460,plain,
( ! [X0: set_Pr1986765409at_nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,edges),X0)) )
| ~ spl155_10
| ~ spl155_154 ),
inference(trivial_inequality_removal,[],[f4457]) ).
thf(f4457,plain,
( ! [X0: set_Pr1986765409at_nat] :
( ( $true != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,edges),X0)) ) )
| ~ spl155_10
| ~ spl155_154 ),
inference(superposition,[],[f2811,f4323]) ).
thf(f5403,plain,
spl155_205,
inference(avatar_split_clause,[],[f2517,f5401]) ).
thf(f5401,plain,
( spl155_205
<=> ! [X2: nat,X1: nat > nat,X3: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(nat,nat,X1,X2)),vAPP(nat,nat,X1,X3)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(sTfun(nat,nat),nat,sK75,X1)),vAPP(sTfun(nat,nat),nat,sK76,X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X2),X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_205])]) ).
thf(f2517,plain,
! [X2: nat,X3: nat,X1: nat > nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(nat,nat,X1,X2)),vAPP(nat,nat,X1,X3)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(sTfun(nat,nat),nat,sK75,X1)),vAPP(sTfun(nat,nat),nat,sK76,X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X2),X3) ) ),
inference(equality_resolution,[],[f2405]) ).
thf(f2405,plain,
! [X2: nat,X3: nat,X0: nat,X1: nat > nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),vAPP(nat,nat,X1,X3)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(sTfun(nat,nat),nat,sK75,X1)),vAPP(sTfun(nat,nat),nat,sK76,X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X2),X3) )
| ( vAPP(nat,nat,X1,X2) != X0 ) ),
inference(definition_unfolding,[],[f1994,f1646,f1646,f1646]) ).
thf(f1994,plain,
! [X2: nat,X3: nat,X0: nat,X1: nat > nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,X1,X3)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,nat),nat,sK75,X1)),vAPP(sTfun(nat,nat),nat,sK76,X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
| ( vAPP(nat,nat,X1,X2) != X0 ) ),
inference(cnf_transformation,[],[f1538]) ).
thf(f5399,plain,
spl155_204,
inference(avatar_split_clause,[],[f2515,f5397]) ).
thf(f5397,plain,
( spl155_204
<=> ! [X2: nat,X1: nat > set_nat,X3: nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(nat,set_nat,X1,X2)),vAPP(nat,set_nat,X1,X3)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(sTfun(nat,set_nat),nat,sK73,X1)),vAPP(sTfun(nat,set_nat),nat,sK74,X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X2),X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_204])]) ).
thf(f2515,plain,
! [X2: nat,X3: nat,X1: nat > set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(nat,set_nat,X1,X2)),vAPP(nat,set_nat,X1,X3)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(sTfun(nat,set_nat),nat,sK73,X1)),vAPP(sTfun(nat,set_nat),nat,sK74,X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X2),X3) ) ),
inference(equality_resolution,[],[f2403]) ).
thf(f2403,plain,
! [X2: nat,X3: nat,X0: set_nat,X1: nat > set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),vAPP(nat,set_nat,X1,X3)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(sTfun(nat,set_nat),nat,sK73,X1)),vAPP(sTfun(nat,set_nat),nat,sK74,X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X2),X3) )
| ( vAPP(nat,set_nat,X1,X2) != X0 ) ),
inference(definition_unfolding,[],[f1992,f1650,f1646,f1646]) ).
thf(f1992,plain,
! [X2: nat,X3: nat,X0: set_nat,X1: nat > set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),vAPP(nat,set_nat,X1,X3)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,set_nat),nat,sK73,X1)),vAPP(sTfun(nat,set_nat),nat,sK74,X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
| ( vAPP(nat,set_nat,X1,X2) != X0 ) ),
inference(cnf_transformation,[],[f1536]) ).
thf(f5395,plain,
spl155_203,
inference(avatar_split_clause,[],[f2513,f5393]) ).
thf(f5393,plain,
( spl155_203
<=> ! [X2: set_nat,X1: set_nat > set_Pr1986765409at_nat,X3: set_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_nat,set_Pr1986765409at_nat,X1,X2)),vAPP(set_nat,set_Pr1986765409at_nat,X1,X3)) )
| ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(sTfun(set_nat,set_Pr1986765409at_nat),set_nat,sK71,X1)),vAPP(sTfun(set_nat,set_Pr1986765409at_nat),set_nat,sK72,X1)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X2),X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_203])]) ).
thf(f2513,plain,
! [X2: set_nat,X3: set_nat,X1: set_nat > set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_nat,set_Pr1986765409at_nat,X1,X2)),vAPP(set_nat,set_Pr1986765409at_nat,X1,X3)) )
| ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(sTfun(set_nat,set_Pr1986765409at_nat),set_nat,sK71,X1)),vAPP(sTfun(set_nat,set_Pr1986765409at_nat),set_nat,sK72,X1)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X2),X3) ) ),
inference(equality_resolution,[],[f2401]) ).
thf(f2401,plain,
! [X2: set_nat,X3: set_nat,X0: set_Pr1986765409at_nat,X1: set_nat > set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),vAPP(set_nat,set_Pr1986765409at_nat,X1,X3)) )
| ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(sTfun(set_nat,set_Pr1986765409at_nat),set_nat,sK71,X1)),vAPP(sTfun(set_nat,set_Pr1986765409at_nat),set_nat,sK72,X1)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X2),X3) )
| ( vAPP(set_nat,set_Pr1986765409at_nat,X1,X2) != X0 ) ),
inference(definition_unfolding,[],[f1990,f1656,f1650,f1650]) ).
thf(f1990,plain,
! [X2: set_nat,X3: set_nat,X0: set_Pr1986765409at_nat,X1: set_nat > set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),vAPP(set_nat,set_Pr1986765409at_nat,X1,X3)) )
| ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(sTfun(set_nat,set_Pr1986765409at_nat),set_nat,sK71,X1)),vAPP(sTfun(set_nat,set_Pr1986765409at_nat),set_nat,sK72,X1)) )
| ( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X3) != $true )
| ( vAPP(set_nat,set_Pr1986765409at_nat,X1,X2) != X0 ) ),
inference(cnf_transformation,[],[f1534]) ).
thf(f5391,plain,
spl155_202,
inference(avatar_split_clause,[],[f2511,f5389]) ).
thf(f5389,plain,
( spl155_202
<=> ! [X2: set_nat,X1: set_nat > nat,X3: set_nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_nat,nat,X1,X2)),vAPP(set_nat,nat,X1,X3)) )
| ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(sTfun(set_nat,nat),set_nat,sK69,X1)),vAPP(sTfun(set_nat,nat),set_nat,sK70,X1)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X2),X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_202])]) ).
thf(f2511,plain,
! [X2: set_nat,X3: set_nat,X1: set_nat > nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_nat,nat,X1,X2)),vAPP(set_nat,nat,X1,X3)) )
| ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(sTfun(set_nat,nat),set_nat,sK69,X1)),vAPP(sTfun(set_nat,nat),set_nat,sK70,X1)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X2),X3) ) ),
inference(equality_resolution,[],[f2399]) ).
thf(f2399,plain,
! [X2: set_nat,X3: set_nat,X0: nat,X1: set_nat > nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),vAPP(set_nat,nat,X1,X3)) )
| ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(sTfun(set_nat,nat),set_nat,sK69,X1)),vAPP(sTfun(set_nat,nat),set_nat,sK70,X1)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X2),X3) )
| ( vAPP(set_nat,nat,X1,X2) != X0 ) ),
inference(definition_unfolding,[],[f1988,f1646,f1650,f1650]) ).
thf(f1988,plain,
! [X2: set_nat,X3: set_nat,X0: nat,X1: set_nat > nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(set_nat,nat,X1,X3)) )
| ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(sTfun(set_nat,nat),set_nat,sK69,X1)),vAPP(sTfun(set_nat,nat),set_nat,sK70,X1)) )
| ( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X3) != $true )
| ( vAPP(set_nat,nat,X1,X2) != X0 ) ),
inference(cnf_transformation,[],[f1532]) ).
thf(f5387,plain,
spl155_201,
inference(avatar_split_clause,[],[f2509,f5385]) ).
thf(f5385,plain,
( spl155_201
<=> ! [X2: set_nat,X1: set_nat > set_nat,X3: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_nat,set_nat,X1,X2)),vAPP(set_nat,set_nat,X1,X3)) )
| ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(sTfun(set_nat,set_nat),set_nat,sK67,X1)),vAPP(sTfun(set_nat,set_nat),set_nat,sK68,X1)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X2),X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_201])]) ).
thf(f2509,plain,
! [X2: set_nat,X3: set_nat,X1: set_nat > set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_nat,set_nat,X1,X2)),vAPP(set_nat,set_nat,X1,X3)) )
| ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(sTfun(set_nat,set_nat),set_nat,sK67,X1)),vAPP(sTfun(set_nat,set_nat),set_nat,sK68,X1)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X2),X3) ) ),
inference(equality_resolution,[],[f2397]) ).
thf(f2397,plain,
! [X2: set_nat,X3: set_nat,X0: set_nat,X1: set_nat > set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),vAPP(set_nat,set_nat,X1,X3)) )
| ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(sTfun(set_nat,set_nat),set_nat,sK67,X1)),vAPP(sTfun(set_nat,set_nat),set_nat,sK68,X1)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X2),X3) )
| ( vAPP(set_nat,set_nat,X1,X2) != X0 ) ),
inference(definition_unfolding,[],[f1986,f1650,f1650,f1650]) ).
thf(f1986,plain,
! [X2: set_nat,X3: set_nat,X0: set_nat,X1: set_nat > set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),vAPP(set_nat,set_nat,X1,X3)) )
| ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(sTfun(set_nat,set_nat),set_nat,sK67,X1)),vAPP(sTfun(set_nat,set_nat),set_nat,sK68,X1)) )
| ( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X3) != $true )
| ( vAPP(set_nat,set_nat,X1,X2) != X0 ) ),
inference(cnf_transformation,[],[f1530]) ).
thf(f5383,plain,
spl155_200,
inference(avatar_split_clause,[],[f2453,f5381]) ).
thf(f5381,plain,
( spl155_200
<=> ! [X0: set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X2)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),X3)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X2),X3) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_200])]) ).
thf(f2453,plain,
! [X2: set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X2)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),X3)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X2),X3) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X1) ) ),
inference(definition_unfolding,[],[f2049,f1656,f1656,f1656]) ).
thf(f2049,plain,
! [X2: set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X2)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),X3)) )
| ( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X2),X3) != $true )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1382]) ).
thf(f1382,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X2)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),X3)) )
| ( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X2),X3) != $true )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1) ) ),
inference(flattening,[],[f1381]) ).
thf(f1381,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X2)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),X3)) )
| ( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X2),X3) != $true )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1) ) ),
inference(ennf_transformation,[],[f963]) ).
thf(f963,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1) )
=> ( ( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X2),X3) = $true )
=> ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X2)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),X3)) ) ) ),
inference(fool_elimination,[],[f962]) ).
thf(f962,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1)
=> ( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X2),X3)
=> vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X2)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),X3)) ) ),
inference(rectify,[],[f300]) ).
thf(f300,axiom,
! [X13: set_Pr1986765409at_nat,X9: set_Pr1986765409at_nat,X12: set_Pr1986765409at_nat,X44: set_Pr1986765409at_nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X13),X9)
=> ( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X12),X44)
=> vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X13),X12)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X9),X44)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_299_inf__mono) ).
thf(f5379,plain,
spl155_199,
inference(avatar_split_clause,[],[f2437,f5377]) ).
thf(f5377,plain,
( spl155_199
<=> ! [X0: nat,X3: nat,X2: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X1),X3)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X2),X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_199])]) ).
thf(f2437,plain,
! [X2: nat,X3: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X1),X3)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X2),X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),X1) ) ),
inference(definition_unfolding,[],[f2033,f1646,f1646,f1646]) ).
thf(f2033,plain,
! [X2: nat,X3: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X1),X3)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1366]) ).
thf(f1366,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X1),X3)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(flattening,[],[f1365]) ).
thf(f1365,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X1),X3)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(ennf_transformation,[],[f947]) ).
thf(f947,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X1),X3)) ) ) ),
inference(fool_elimination,[],[f946]) ).
thf(f946,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X1),X3)) ) ),
inference(rectify,[],[f302]) ).
thf(f302,axiom,
! [X13: nat,X9: nat,X12: nat,X44: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X13),X9)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X12),X44)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X13),X12)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X9),X44)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_301_inf__mono) ).
thf(f5375,plain,
spl155_198,
inference(avatar_split_clause,[],[f2423,f5373]) ).
thf(f5373,plain,
( spl155_198
<=> ! [X0: set_nat,X3: set_nat,X2: set_nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X2)),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),X3)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X2),X3) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_198])]) ).
thf(f2423,plain,
! [X2: set_nat,X3: set_nat,X0: set_nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X2)),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),X3)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X2),X3) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),X1) ) ),
inference(definition_unfolding,[],[f2019,f1650,f1650,f1650]) ).
thf(f2019,plain,
! [X2: set_nat,X3: set_nat,X0: set_nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X2)),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),X3)) )
| ( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X3) != $true )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1350]) ).
thf(f1350,plain,
! [X0: set_nat,X1: set_nat,X2: set_nat,X3: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X2)),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),X3)) )
| ( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X3) != $true )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1) ) ),
inference(flattening,[],[f1349]) ).
thf(f1349,plain,
! [X0: set_nat,X1: set_nat,X2: set_nat,X3: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X2)),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),X3)) )
| ( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X3) != $true )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1) ) ),
inference(ennf_transformation,[],[f931]) ).
thf(f931,plain,
! [X0: set_nat,X1: set_nat,X2: set_nat,X3: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1) )
=> ( ( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X3) = $true )
=> ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X2)),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),X3)) ) ) ),
inference(fool_elimination,[],[f930]) ).
thf(f930,plain,
! [X0: set_nat,X1: set_nat,X2: set_nat,X3: set_nat] :
( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1)
=> ( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X3)
=> vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X2)),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),X3)) ) ),
inference(rectify,[],[f301]) ).
thf(f301,axiom,
! [X13: set_nat,X9: set_nat,X12: set_nat,X44: set_nat] :
( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X13),X9)
=> ( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X12),X44)
=> vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X13),X12)),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X9),X44)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_300_inf__mono) ).
thf(f5296,plain,
spl155_197,
inference(avatar_split_clause,[],[f2374,f5294]) ).
thf(f5294,plain,
( spl155_197
<=> ! [X2: set_Pr1986765409at_nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),X2)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X2) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_197])]) ).
thf(f2374,plain,
! [X2: set_Pr1986765409at_nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),X2)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X2) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X1) ) ),
inference(definition_unfolding,[],[f1942,f1656,f1656,f1656]) ).
thf(f1942,plain,
! [X2: set_Pr1986765409at_nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),X2)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X2) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1286]) ).
thf(f1286,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),X2)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X2) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1) ) ),
inference(flattening,[],[f1285]) ).
thf(f1285,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),X2)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X2) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1) ) ),
inference(ennf_transformation,[],[f847]) ).
thf(f847,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1) )
=> ( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X2) )
=> ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),X2)) ) ) ),
inference(fool_elimination,[],[f846]) ).
thf(f846,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1)
=> ( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X2)
=> vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),X2)) ) ),
inference(rectify,[],[f261]) ).
thf(f261,axiom,
! [X5: set_Pr1986765409at_nat,X21: set_Pr1986765409at_nat,X22: set_Pr1986765409at_nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X5),X21)
=> ( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X5),X22)
=> vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X5),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X21),X22)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_260_inf__greatest) ).
thf(f5292,plain,
spl155_196,
inference(avatar_split_clause,[],[f2360,f5290]) ).
thf(f5290,plain,
( spl155_196
<=> ! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X1),X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_196])]) ).
thf(f2360,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X1),X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),X1) ) ),
inference(definition_unfolding,[],[f1927,f1646,f1646,f1646]) ).
thf(f1927,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X1),X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1260]) ).
thf(f1260,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X1),X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(flattening,[],[f1259]) ).
thf(f1259,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X1),X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(ennf_transformation,[],[f817]) ).
thf(f817,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X1),X2)) ) ) ),
inference(fool_elimination,[],[f816]) ).
thf(f816,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X1),X2)) ) ),
inference(rectify,[],[f263]) ).
thf(f263,axiom,
! [X5: nat,X21: nat,X22: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X5),X21)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X5),X22)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X5),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X21),X22)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_262_inf__greatest) ).
thf(f5288,plain,
spl155_195,
inference(avatar_split_clause,[],[f2346,f5286]) ).
thf(f5286,plain,
( spl155_195
<=> ! [X2: set_nat,X0: set_nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),X2)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),X2) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_195])]) ).
thf(f2346,plain,
! [X2: set_nat,X0: set_nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),X2)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),X2) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),X1) ) ),
inference(definition_unfolding,[],[f1912,f1650,f1650,f1650]) ).
thf(f1912,plain,
! [X2: set_nat,X0: set_nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),X2)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X2) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1234]) ).
thf(f1234,plain,
! [X0: set_nat,X1: set_nat,X2: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),X2)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X2) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1) ) ),
inference(flattening,[],[f1233]) ).
thf(f1233,plain,
! [X0: set_nat,X1: set_nat,X2: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),X2)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X2) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1) ) ),
inference(ennf_transformation,[],[f787]) ).
thf(f787,plain,
! [X0: set_nat,X1: set_nat,X2: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1) )
=> ( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X2) )
=> ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),X2)) ) ) ),
inference(fool_elimination,[],[f786]) ).
thf(f786,plain,
! [X0: set_nat,X1: set_nat,X2: set_nat] :
( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1)
=> ( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X2)
=> vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),X2)) ) ),
inference(rectify,[],[f265]) ).
thf(f265,axiom,
! [X13: set_nat,X12: set_nat,X9: set_nat] :
( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X13),X12)
=> ( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X13),X9)
=> vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X13),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X12),X9)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_264_inf_OboundedI) ).
thf(f5223,plain,
spl155_194,
inference(avatar_split_clause,[],[f2370,f5221]) ).
thf(f5221,plain,
( spl155_194
<=> ! [X2: set_Pr1986765409at_nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X2) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X1),X2) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_194])]) ).
thf(f2370,plain,
! [X2: set_Pr1986765409at_nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X2) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X1),X2) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X1) ) ),
inference(definition_unfolding,[],[f1938,f1656,f1656,f1656]) ).
thf(f1938,plain,
! [X2: set_Pr1986765409at_nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X2) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X1),X2) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1278]) ).
thf(f1278,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X2) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X1),X2) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1) ) ),
inference(flattening,[],[f1277]) ).
thf(f1277,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X2) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X1),X2) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1) ) ),
inference(ennf_transformation,[],[f839]) ).
thf(f839,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1) )
=> ( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X1),X2) )
=> ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X2) ) ) ),
inference(fool_elimination,[],[f838]) ).
thf(f838,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1)
=> ( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X1),X2)
=> vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X2) ) ),
inference(rectify,[],[f42]) ).
thf(f42,axiom,
! [X5: set_Pr1986765409at_nat,X21: set_Pr1986765409at_nat,X22: set_Pr1986765409at_nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X5),X21)
=> ( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X21),X22)
=> vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X5),X22) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_order__trans) ).
thf(f5219,plain,
spl155_193,
inference(avatar_split_clause,[],[f2357,f5217]) ).
thf(f5217,plain,
( spl155_193
<=> ! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X1),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_193])]) ).
thf(f2357,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X1),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),X1) ) ),
inference(definition_unfolding,[],[f1924,f1646,f1646,f1646]) ).
thf(f1924,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1254]) ).
thf(f1254,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(flattening,[],[f1253]) ).
thf(f1253,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(ennf_transformation,[],[f811]) ).
thf(f811,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) ) ) ),
inference(fool_elimination,[],[f810]) ).
thf(f810,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) ) ),
inference(rectify,[],[f44]) ).
thf(f44,axiom,
! [X5: nat,X21: nat,X22: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X5),X21)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X21),X22)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X5),X22) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_order__trans) ).
thf(f5215,plain,
spl155_192,
inference(avatar_split_clause,[],[f2342,f5213]) ).
thf(f5213,plain,
( spl155_192
<=> ! [X2: set_nat,X0: set_nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X2),X1) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X2),X0) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_192])]) ).
thf(f2342,plain,
! [X2: set_nat,X0: set_nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X2),X1) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X2),X0) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),X1) ) ),
inference(definition_unfolding,[],[f1908,f1650,f1650,f1650]) ).
thf(f1908,plain,
! [X2: set_nat,X0: set_nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X1) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X0) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1226]) ).
thf(f1226,plain,
! [X0: set_nat,X1: set_nat,X2: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X1) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X0) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1) ) ),
inference(flattening,[],[f1225]) ).
thf(f1225,plain,
! [X0: set_nat,X1: set_nat,X2: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X1) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X0) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1) ) ),
inference(ennf_transformation,[],[f779]) ).
thf(f779,plain,
! [X0: set_nat,X1: set_nat,X2: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1) )
=> ( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X0) )
=> ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X1) ) ) ),
inference(fool_elimination,[],[f778]) ).
thf(f778,plain,
! [X0: set_nat,X1: set_nat,X2: set_nat] :
( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1)
=> ( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X0)
=> vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X1) ) ),
inference(rectify,[],[f36]) ).
thf(f36,axiom,
! [X12: set_nat,X13: set_nat,X9: set_nat] :
( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X12),X13)
=> ( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X9),X12)
=> vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X9),X13) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_dual__order_Otrans) ).
thf(f5211,plain,
( spl155_191
| ~ spl155_2
| ~ spl155_181 ),
inference(avatar_split_clause,[],[f5185,f4909,f2739,f5209]) ).
thf(f5185,plain,
( ! [X0: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),edges)) )
| ( $false = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),X0) ) )
| ~ spl155_2
| ~ spl155_181 ),
inference(trivial_inequality_removal,[],[f5184]) ).
thf(f5184,plain,
( ! [X0: set_Pr1986765409at_nat] :
( ( $true != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),edges)) )
| ( $false = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),X0) ) )
| ~ spl155_2
| ~ spl155_181 ),
inference(superposition,[],[f4910,f2740]) ).
thf(f5207,plain,
spl155_190,
inference(avatar_split_clause,[],[f2110,f5204]) ).
thf(f5204,plain,
( spl155_190
<=> ( vEQ(set_Pr1986765409at_nat) = vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(sTfun(set_Pr1986765409at_nat,$o),sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun($o,$o))),sTfun(set_Pr1986765409at_nat,sTfun(sTfun(set_Pr1986765409at_nat,$o),sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun($o,$o)),sTfun(sTfun(set_Pr1986765409at_nat,$o),sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun($o,$o))),sTfun(set_Pr1986765409at_nat,sTfun(sTfun(set_Pr1986765409at_nat,$o),sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun($o,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,$o),sTfun(set_Pr1986765409at_nat,sTfun($o,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(set_Pr1986765409at_nat,$o),sTfun(set_Pr1986765409at_nat,sTfun($o,$o))),bCOMB,vAND)),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB)))),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),cCOMB,vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_190])]) ).
thf(f2110,plain,
vEQ(set_Pr1986765409at_nat) = vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(sTfun(set_Pr1986765409at_nat,$o),sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun($o,$o))),sTfun(set_Pr1986765409at_nat,sTfun(sTfun(set_Pr1986765409at_nat,$o),sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun($o,$o)),sTfun(sTfun(set_Pr1986765409at_nat,$o),sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun($o,$o))),sTfun(set_Pr1986765409at_nat,sTfun(sTfun(set_Pr1986765409at_nat,$o),sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun($o,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,$o),sTfun(set_Pr1986765409at_nat,sTfun($o,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(set_Pr1986765409at_nat,$o),sTfun(set_Pr1986765409at_nat,sTfun($o,$o))),bCOMB,vAND)),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB)))),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),cCOMB,vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB))),
inference(definition_unfolding,[],[f1641,f1656,f1656]) ).
thf(f1641,plain,
vEQ(set_Pr1986765409at_nat) = vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(sTfun(set_Pr1986765409at_nat,$o),sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun($o,$o))),sTfun(set_Pr1986765409at_nat,sTfun(sTfun(set_Pr1986765409at_nat,$o),sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun($o,$o)),sTfun(sTfun(set_Pr1986765409at_nat,$o),sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun($o,$o))),sTfun(set_Pr1986765409at_nat,sTfun(sTfun(set_Pr1986765409at_nat,$o),sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun($o,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,$o),sTfun(set_Pr1986765409at_nat,sTfun($o,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(set_Pr1986765409at_nat,$o),sTfun(set_Pr1986765409at_nat,sTfun($o,$o))),bCOMB,vAND)),ord_le841296385at_nat))),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),cCOMB,ord_le841296385at_nat)),
inference(cnf_transformation,[],[f377]) ).
thf(f377,plain,
vEQ(set_Pr1986765409at_nat) = vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(sTfun(set_Pr1986765409at_nat,$o),sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun($o,$o))),sTfun(set_Pr1986765409at_nat,sTfun(sTfun(set_Pr1986765409at_nat,$o),sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun($o,$o)),sTfun(sTfun(set_Pr1986765409at_nat,$o),sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun($o,$o))),sTfun(set_Pr1986765409at_nat,sTfun(sTfun(set_Pr1986765409at_nat,$o),sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun($o,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,$o),sTfun(set_Pr1986765409at_nat,sTfun($o,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(set_Pr1986765409at_nat,$o),sTfun(set_Pr1986765409at_nat,sTfun($o,$o))),bCOMB,vAND)),ord_le841296385at_nat))),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),cCOMB,ord_le841296385at_nat)),
inference(fool_elimination,[],[f376]) ).
thf(f376,plain,
( ( ^ [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] : ( X0 = X1 ) )
= ( ^ [X2: set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X3),X2)
& vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X2),X3) ) ) ),
inference(rectify,[],[f54]) ).
thf(f54,axiom,
( ( ^ [X14: set_Pr1986765409at_nat,X15: set_Pr1986765409at_nat] : ( X14 = X15 ) )
= ( ^ [X16: set_Pr1986765409at_nat,X17: set_Pr1986765409at_nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X17),X16)
& vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X16),X17) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_order__class_Oorder_Oeq__iff) ).
thf(f5202,plain,
spl155_189,
inference(avatar_split_clause,[],[f2109,f5199]) ).
thf(f5199,plain,
( spl155_189
<=> ( vEQ(set_Pr1986765409at_nat) = vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(sTfun(set_Pr1986765409at_nat,$o),sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun($o,$o))),sTfun(set_Pr1986765409at_nat,sTfun(sTfun(set_Pr1986765409at_nat,$o),sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun($o,$o)),sTfun(sTfun(set_Pr1986765409at_nat,$o),sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun($o,$o))),sTfun(set_Pr1986765409at_nat,sTfun(sTfun(set_Pr1986765409at_nat,$o),sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun($o,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,$o),sTfun(set_Pr1986765409at_nat,sTfun($o,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(set_Pr1986765409at_nat,$o),sTfun(set_Pr1986765409at_nat,sTfun($o,$o))),bCOMB,vAND)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),cCOMB,vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB))))),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_189])]) ).
thf(f2109,plain,
vEQ(set_Pr1986765409at_nat) = vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(sTfun(set_Pr1986765409at_nat,$o),sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun($o,$o))),sTfun(set_Pr1986765409at_nat,sTfun(sTfun(set_Pr1986765409at_nat,$o),sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun($o,$o)),sTfun(sTfun(set_Pr1986765409at_nat,$o),sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun($o,$o))),sTfun(set_Pr1986765409at_nat,sTfun(sTfun(set_Pr1986765409at_nat,$o),sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun($o,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,$o),sTfun(set_Pr1986765409at_nat,sTfun($o,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(set_Pr1986765409at_nat,$o),sTfun(set_Pr1986765409at_nat,sTfun($o,$o))),bCOMB,vAND)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),cCOMB,vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB))))),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB)),
inference(definition_unfolding,[],[f1640,f1656,f1656]) ).
thf(f1640,plain,
vEQ(set_Pr1986765409at_nat) = vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(sTfun(set_Pr1986765409at_nat,$o),sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun($o,$o))),sTfun(set_Pr1986765409at_nat,sTfun(sTfun(set_Pr1986765409at_nat,$o),sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun($o,$o)),sTfun(sTfun(set_Pr1986765409at_nat,$o),sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun($o,$o))),sTfun(set_Pr1986765409at_nat,sTfun(sTfun(set_Pr1986765409at_nat,$o),sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun($o,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,$o),sTfun(set_Pr1986765409at_nat,sTfun($o,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(set_Pr1986765409at_nat,$o),sTfun(set_Pr1986765409at_nat,sTfun($o,$o))),bCOMB,vAND)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),cCOMB,ord_le841296385at_nat)))),ord_le841296385at_nat),
inference(cnf_transformation,[],[f375]) ).
thf(f375,plain,
vEQ(set_Pr1986765409at_nat) = vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(sTfun(set_Pr1986765409at_nat,$o),sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun($o,$o))),sTfun(set_Pr1986765409at_nat,sTfun(sTfun(set_Pr1986765409at_nat,$o),sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun($o,$o)),sTfun(sTfun(set_Pr1986765409at_nat,$o),sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun($o,$o))),sTfun(set_Pr1986765409at_nat,sTfun(sTfun(set_Pr1986765409at_nat,$o),sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun($o,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,$o),sTfun(set_Pr1986765409at_nat,sTfun($o,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(set_Pr1986765409at_nat,$o),sTfun(set_Pr1986765409at_nat,sTfun($o,$o))),bCOMB,vAND)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),cCOMB,ord_le841296385at_nat)))),ord_le841296385at_nat),
inference(fool_elimination,[],[f374]) ).
thf(f374,plain,
( ( ^ [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] : ( X0 = X1 ) )
= ( ^ [X2: set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X2),X3)
& vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X3),X2) ) ) ),
inference(rectify,[],[f32]) ).
thf(f32,axiom,
( ( ^ [X14: set_Pr1986765409at_nat,X15: set_Pr1986765409at_nat] : ( X14 = X15 ) )
= ( ^ [X16: set_Pr1986765409at_nat,X17: set_Pr1986765409at_nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X16),X17)
& vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X17),X16) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_dual__order_Oeq__iff) ).
thf(f5197,plain,
spl155_188,
inference(avatar_split_clause,[],[f2107,f5194]) ).
thf(f5194,plain,
( spl155_188
<=> ( vEQ(nat) = vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun($o,$o))),sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun($o,$o))),sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vAND)),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB)))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_188])]) ).
thf(f2107,plain,
vEQ(nat) = vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun($o,$o))),sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun($o,$o))),sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vAND)),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB)))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB))),
inference(definition_unfolding,[],[f1638,f1646,f1646]) ).
thf(f1638,plain,
vEQ(nat) = vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun($o,$o))),sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun($o,$o))),sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vAND)),ord_less_eq_nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,ord_less_eq_nat)),
inference(cnf_transformation,[],[f371]) ).
thf(f371,plain,
vEQ(nat) = vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun($o,$o))),sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun($o,$o))),sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vAND)),ord_less_eq_nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,ord_less_eq_nat)),
inference(fool_elimination,[],[f370]) ).
thf(f370,plain,
( ( ^ [X0: nat,X1: nat] : ( X0 = X1 ) )
= ( ^ [X2: nat,X3: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X2)
& vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) ) ) ),
inference(rectify,[],[f56]) ).
thf(f56,axiom,
( ( ^ [X14: nat,X15: nat] : ( X14 = X15 ) )
= ( ^ [X16: nat,X17: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X17),X16)
& vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X16),X17) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_order__class_Oorder_Oeq__iff) ).
thf(f5192,plain,
spl155_187,
inference(avatar_split_clause,[],[f2106,f5189]) ).
thf(f5189,plain,
( spl155_187
<=> ( vEQ(nat) = vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun($o,$o))),sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun($o,$o))),sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vAND)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB))))),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_187])]) ).
thf(f2106,plain,
vEQ(nat) = vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun($o,$o))),sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun($o,$o))),sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vAND)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB))))),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB)),
inference(definition_unfolding,[],[f1637,f1646,f1646]) ).
thf(f1637,plain,
vEQ(nat) = vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun($o,$o))),sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun($o,$o))),sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vAND)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,ord_less_eq_nat)))),ord_less_eq_nat),
inference(cnf_transformation,[],[f369]) ).
thf(f369,plain,
vEQ(nat) = vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun($o,$o))),sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun($o,$o))),sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vAND)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,ord_less_eq_nat)))),ord_less_eq_nat),
inference(fool_elimination,[],[f368]) ).
thf(f368,plain,
( ( ^ [X0: nat,X1: nat] : ( X0 = X1 ) )
= ( ^ [X2: nat,X3: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3)
& vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X2) ) ) ),
inference(rectify,[],[f34]) ).
thf(f34,axiom,
( ( ^ [X14: nat,X15: nat] : ( X14 = X15 ) )
= ( ^ [X16: nat,X17: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X16),X17)
& vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X17),X16) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_dual__order_Oeq__iff) ).
thf(f5181,plain,
spl155_186,
inference(avatar_split_clause,[],[f2105,f5178]) ).
thf(f5178,plain,
( spl155_186
<=> ( vEQ(set_nat) = vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(sTfun(set_nat,$o),sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(set_nat,$o),sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun($o,$o)),sTfun(sTfun(set_nat,$o),sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(set_nat,$o),sTfun(set_nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,sTfun($o,$o))),vAPP(sTfun(sTfun(set_nat,$o),sTfun(set_nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(set_nat,$o),sTfun(set_nat,sTfun($o,$o))),bCOMB,vAND)),vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o)),cCOMB,vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB))))),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_186])]) ).
thf(f2105,plain,
vEQ(set_nat) = vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(sTfun(set_nat,$o),sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(set_nat,$o),sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun($o,$o)),sTfun(sTfun(set_nat,$o),sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(set_nat,$o),sTfun(set_nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,sTfun($o,$o))),vAPP(sTfun(sTfun(set_nat,$o),sTfun(set_nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(set_nat,$o),sTfun(set_nat,sTfun($o,$o))),bCOMB,vAND)),vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o)),cCOMB,vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB))))),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB)),
inference(definition_unfolding,[],[f1636,f1650,f1650]) ).
thf(f1636,plain,
vEQ(set_nat) = vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(sTfun(set_nat,$o),sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(set_nat,$o),sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun($o,$o)),sTfun(sTfun(set_nat,$o),sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(set_nat,$o),sTfun(set_nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,sTfun($o,$o))),vAPP(sTfun(sTfun(set_nat,$o),sTfun(set_nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(set_nat,$o),sTfun(set_nat,sTfun($o,$o))),bCOMB,vAND)),vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o)),cCOMB,ord_less_eq_set_nat)))),ord_less_eq_set_nat),
inference(cnf_transformation,[],[f367]) ).
thf(f367,plain,
vEQ(set_nat) = vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(sTfun(set_nat,$o),sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(set_nat,$o),sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun($o,$o)),sTfun(sTfun(set_nat,$o),sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(set_nat,$o),sTfun(set_nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,sTfun($o,$o))),vAPP(sTfun(sTfun(set_nat,$o),sTfun(set_nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(set_nat,$o),sTfun(set_nat,sTfun($o,$o))),bCOMB,vAND)),vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o)),cCOMB,ord_less_eq_set_nat)))),ord_less_eq_set_nat),
inference(fool_elimination,[],[f366]) ).
thf(f366,plain,
( ( ^ [X0: set_nat,X1: set_nat] : ( X0 = X1 ) )
= ( ^ [X2: set_nat,X3: set_nat] :
( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X3)
& vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X3),X2) ) ) ),
inference(rectify,[],[f33]) ).
thf(f33,axiom,
( ( ^ [X14: set_nat,X15: set_nat] : ( X14 = X15 ) )
= ( ^ [X16: set_nat,X17: set_nat] :
( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X16),X17)
& vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X17),X16) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_dual__order_Oeq__iff) ).
thf(f5176,plain,
spl155_185,
inference(avatar_split_clause,[],[f2102,f5173]) ).
thf(f5173,plain,
( spl155_185
<=> ( vEQ(set_nat) = vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(sTfun(set_nat,$o),sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(set_nat,$o),sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun($o,$o)),sTfun(sTfun(set_nat,$o),sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(set_nat,$o),sTfun(set_nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,sTfun($o,$o))),vAPP(sTfun(sTfun(set_nat,$o),sTfun(set_nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(set_nat,$o),sTfun(set_nat,sTfun($o,$o))),bCOMB,vAND)),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB)))),vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o)),cCOMB,vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_185])]) ).
thf(f2102,plain,
vEQ(set_nat) = vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(sTfun(set_nat,$o),sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(set_nat,$o),sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun($o,$o)),sTfun(sTfun(set_nat,$o),sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(set_nat,$o),sTfun(set_nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,sTfun($o,$o))),vAPP(sTfun(sTfun(set_nat,$o),sTfun(set_nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(set_nat,$o),sTfun(set_nat,sTfun($o,$o))),bCOMB,vAND)),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB)))),vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o)),cCOMB,vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB))),
inference(definition_unfolding,[],[f1633,f1650,f1650]) ).
thf(f1633,plain,
vEQ(set_nat) = vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(sTfun(set_nat,$o),sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(set_nat,$o),sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun($o,$o)),sTfun(sTfun(set_nat,$o),sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(set_nat,$o),sTfun(set_nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,sTfun($o,$o))),vAPP(sTfun(sTfun(set_nat,$o),sTfun(set_nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(set_nat,$o),sTfun(set_nat,sTfun($o,$o))),bCOMB,vAND)),ord_less_eq_set_nat))),vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o)),cCOMB,ord_less_eq_set_nat)),
inference(cnf_transformation,[],[f361]) ).
thf(f361,plain,
vEQ(set_nat) = vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(sTfun(set_nat,$o),sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(set_nat,$o),sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun($o,$o)),sTfun(sTfun(set_nat,$o),sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun($o,$o))),sTfun(set_nat,sTfun(sTfun(set_nat,$o),sTfun(set_nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,sTfun($o,$o))),vAPP(sTfun(sTfun(set_nat,$o),sTfun(set_nat,sTfun($o,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(set_nat,$o),sTfun(set_nat,sTfun($o,$o))),bCOMB,vAND)),ord_less_eq_set_nat))),vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o)),cCOMB,ord_less_eq_set_nat)),
inference(fool_elimination,[],[f360]) ).
thf(f360,plain,
( ( ^ [X0: set_nat,X1: set_nat] : ( X0 = X1 ) )
= ( ^ [X2: set_nat,X3: set_nat] :
( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X3),X2)
& vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X3) ) ) ),
inference(rectify,[],[f55]) ).
thf(f55,axiom,
( ( ^ [X14: set_nat,X15: set_nat] : ( X14 = X15 ) )
= ( ^ [X16: set_nat,X17: set_nat] :
( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X17),X16)
& vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X16),X17) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_order__class_Oorder_Oeq__iff) ).
thf(f5021,plain,
spl155_184,
inference(avatar_split_clause,[],[f2321,f5019]) ).
thf(f5019,plain,
( spl155_184
<=> ! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),X1) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X1),X2) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP5,X2),X1),X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP4,X0),X2),X1) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP3,X1),X0),X2) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP2,X0),X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_184])]) ).
thf(f2321,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),X1) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X1),X2) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP5,X2),X1),X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP4,X0),X2),X1) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP3,X1),X0),X2) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP2,X0),X1),X2) ) ),
inference(definition_unfolding,[],[f1881,f1646,f1646]) ).
thf(f1881,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP5,X2),X1),X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP4,X0),X2),X1) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP3,X1),X0),X2) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP2,X0),X1),X2) ) ),
inference(cnf_transformation,[],[f1436]) ).
thf(f1436,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X0) ) )
| ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X0) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP5,X2),X1),X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP4,X0),X2),X1) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP3,X1),X0),X2) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP2,X0),X1),X2) ) ),
inference(definition_folding,[],[f1207,f1435,f1434,f1433,f1432]) ).
thf(f1432,plain,
! [X2: nat,X1: nat,X0: nat] :
( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP2,X0),X1),X2) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f1433,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP3,X1),X0),X2) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f1434,plain,
! [X1: nat,X2: nat,X0: nat] :
( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X1) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP4,X0),X2),X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f1435,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X1) ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP5,X2),X1),X0) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f1207,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X0) ) )
| ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X0) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) )
| ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X1) ) )
| ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X1) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) ) )
| ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) ) )
| ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ) ),
inference(flattening,[],[f1206]) ).
thf(f1206,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X0) ) )
| ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X0) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) )
| ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X1) ) )
| ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X1) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) ) )
| ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) ) )
| ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ) ),
inference(ennf_transformation,[],[f1050]) ).
thf(f1050,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
=> ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) )
=> ( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) )
=> ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) ) )
=> ( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) )
=> ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X1) ) )
=> ( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X1) )
=> ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) ) )
=> ( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
=> ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X0) ) )
=> ~ ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X0) )
=> ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ) ) ) ) ) ),
inference(flattening,[],[f757]) ).
thf(f757,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
=> ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) )
=> ( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) )
=> ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) ) )
=> ( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) )
=> ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X1) ) )
=> ( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X1) )
=> ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) ) )
=> ( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
=> ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X0) ) )
=> ~ ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X0) )
=> ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f756]) ).
thf(f756,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1)
=> ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
=> ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0)
=> ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) )
=> ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2)
=> ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X1) )
=> ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X1)
=> ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) )
=> ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2)
=> ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X0) )
=> ~ ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X0)
=> ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ) ) ) ) ),
inference(rectify,[],[f60]) ).
thf(f60,axiom,
! [X5: nat,X21: nat,X22: nat] :
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X5),X21)
=> ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X21),X22) )
=> ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X21),X5)
=> ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X5),X22) )
=> ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X5),X22)
=> ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X22),X21) )
=> ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X22),X21)
=> ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X21),X5) )
=> ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X21),X22)
=> ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X22),X5) )
=> ~ ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X22),X5)
=> ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X5),X21) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_le__cases3) ).
thf(f4975,plain,
spl155_183,
inference(avatar_split_clause,[],[f2452,f4973]) ).
thf(f4973,plain,
( spl155_183
<=> ! [X0: set_Pr1986765409at_nat,X3: product_prod_nat_nat > $o,X2: product_prod_nat_nat > $o,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X2))),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X3))) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(sTfun(product_prod_nat_nat,$o),sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),vAPP(sTfun(product_prod_nat_nat,$o),sTfun(sTfun(product_prod_nat_nat,$o),sTfun(set_Pr1986765409at_nat,product_prod_nat_nat)),sK126,X3),X2),X0)),X0) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_183])]) ).
thf(f2452,plain,
! [X2: product_prod_nat_nat > $o,X3: product_prod_nat_nat > $o,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X2))),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X3))) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(sTfun(product_prod_nat_nat,$o),sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),vAPP(sTfun(product_prod_nat_nat,$o),sTfun(sTfun(product_prod_nat_nat,$o),sTfun(set_Pr1986765409at_nat,product_prod_nat_nat)),sK126,X3),X2),X0)),X0) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X1) ) ),
inference(definition_unfolding,[],[f2046,f1656,f1656]) ).
thf(f2046,plain,
! [X2: product_prod_nat_nat > $o,X3: product_prod_nat_nat > $o,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X2))),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X3))) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(sTfun(product_prod_nat_nat,$o),sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),vAPP(sTfun(product_prod_nat_nat,$o),sTfun(sTfun(product_prod_nat_nat,$o),sTfun(set_Pr1986765409at_nat,product_prod_nat_nat)),sK126,X3),X2),X0)),X0) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1586]) ).
thf(f1586,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat,X2: product_prod_nat_nat > $o,X3: product_prod_nat_nat > $o] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X2))),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X3))) )
| ( ( $true != vAPP(product_prod_nat_nat,$o,X3,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(sTfun(product_prod_nat_nat,$o),sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),vAPP(sTfun(product_prod_nat_nat,$o),sTfun(sTfun(product_prod_nat_nat,$o),sTfun(set_Pr1986765409at_nat,product_prod_nat_nat)),sK126,X3),X2),X0)) )
& ( $true = vAPP(product_prod_nat_nat,$o,X2,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(sTfun(product_prod_nat_nat,$o),sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),vAPP(sTfun(product_prod_nat_nat,$o),sTfun(sTfun(product_prod_nat_nat,$o),sTfun(set_Pr1986765409at_nat,product_prod_nat_nat)),sK126,X3),X2),X0)) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(sTfun(product_prod_nat_nat,$o),sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),vAPP(sTfun(product_prod_nat_nat,$o),sTfun(sTfun(product_prod_nat_nat,$o),sTfun(set_Pr1986765409at_nat,product_prod_nat_nat)),sK126,X3),X2),X0)),X0) ) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK126])],[f1380,f1585]) ).
thf(f1585,plain,
! [X0: set_Pr1986765409at_nat,X2: product_prod_nat_nat > $o,X3: product_prod_nat_nat > $o] :
( ? [X4: product_prod_nat_nat] :
( ( $true != vAPP(product_prod_nat_nat,$o,X3,X4) )
& ( $true = vAPP(product_prod_nat_nat,$o,X2,X4) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X4),X0) ) )
=> ( ( $true != vAPP(product_prod_nat_nat,$o,X3,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(sTfun(product_prod_nat_nat,$o),sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),vAPP(sTfun(product_prod_nat_nat,$o),sTfun(sTfun(product_prod_nat_nat,$o),sTfun(set_Pr1986765409at_nat,product_prod_nat_nat)),sK126,X3),X2),X0)) )
& ( $true = vAPP(product_prod_nat_nat,$o,X2,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(sTfun(product_prod_nat_nat,$o),sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),vAPP(sTfun(product_prod_nat_nat,$o),sTfun(sTfun(product_prod_nat_nat,$o),sTfun(set_Pr1986765409at_nat,product_prod_nat_nat)),sK126,X3),X2),X0)) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(sTfun(product_prod_nat_nat,$o),sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),vAPP(sTfun(product_prod_nat_nat,$o),sTfun(sTfun(product_prod_nat_nat,$o),sTfun(set_Pr1986765409at_nat,product_prod_nat_nat)),sK126,X3),X2),X0)),X0) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1380,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat,X2: product_prod_nat_nat > $o,X3: product_prod_nat_nat > $o] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X2))),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X3))) )
| ? [X4: product_prod_nat_nat] :
( ( $true != vAPP(product_prod_nat_nat,$o,X3,X4) )
& ( $true = vAPP(product_prod_nat_nat,$o,X2,X4) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X4),X0) ) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1) ) ),
inference(flattening,[],[f1379]) ).
thf(f1379,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat,X2: product_prod_nat_nat > $o,X3: product_prod_nat_nat > $o] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X2))),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X3))) )
| ? [X4: product_prod_nat_nat] :
( ( $true != vAPP(product_prod_nat_nat,$o,X3,X4) )
& ( $true = vAPP(product_prod_nat_nat,$o,X2,X4) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X4),X0) ) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1) ) ),
inference(ennf_transformation,[],[f961]) ).
thf(f961,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat,X2: product_prod_nat_nat > $o,X3: product_prod_nat_nat > $o] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1) )
=> ( ! [X4: product_prod_nat_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X4),X0) )
=> ( ( $true = vAPP(product_prod_nat_nat,$o,X2,X4) )
=> ( $true = vAPP(product_prod_nat_nat,$o,X3,X4) ) ) )
=> ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X2))),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X3))) ) ) ),
inference(fool_elimination,[],[f960]) ).
thf(f960,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat,X2: product_prod_nat_nat > $o,X3: product_prod_nat_nat > $o] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1)
=> ( ! [X4: product_prod_nat_nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X4),X0)
=> ( vAPP(product_prod_nat_nat,$o,X2,X4)
=> vAPP(product_prod_nat_nat,$o,X3,X4) ) )
=> vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X2))),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X3))) ) ),
inference(rectify,[],[f182]) ).
thf(f182,axiom,
! [X2: set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat,X18: product_prod_nat_nat > $o,X27: product_prod_nat_nat > $o] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X2),X3)
=> ( ! [X4: product_prod_nat_nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X4),X2)
=> ( vAPP(product_prod_nat_nat,$o,X18,X4)
=> vAPP(product_prod_nat_nat,$o,X27,X4) ) )
=> vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X2),vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X18))),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X3),vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X27))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_Int__Collect__mono) ).
thf(f4971,plain,
spl155_182,
inference(avatar_split_clause,[],[f2422,f4969]) ).
thf(f4969,plain,
( spl155_182
<=> ! [X0: set_nat,X3: nat > $o,X2: nat > $o,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),vAPP(sTfun(nat,$o),set_nat,collect_nat,X2))),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),vAPP(sTfun(nat,$o),set_nat,collect_nat,X3))) )
| ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,vAPP(set_nat,nat,vAPP(sTfun(nat,$o),sTfun(set_nat,nat),vAPP(sTfun(nat,$o),sTfun(sTfun(nat,$o),sTfun(set_nat,nat)),sK101,X3),X2),X0)),X0) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_182])]) ).
thf(f2422,plain,
! [X2: nat > $o,X3: nat > $o,X0: set_nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),vAPP(sTfun(nat,$o),set_nat,collect_nat,X2))),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),vAPP(sTfun(nat,$o),set_nat,collect_nat,X3))) )
| ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,vAPP(set_nat,nat,vAPP(sTfun(nat,$o),sTfun(set_nat,nat),vAPP(sTfun(nat,$o),sTfun(sTfun(nat,$o),sTfun(set_nat,nat)),sK101,X3),X2),X0)),X0) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),X1) ) ),
inference(definition_unfolding,[],[f2016,f1650,f1650]) ).
thf(f2016,plain,
! [X2: nat > $o,X3: nat > $o,X0: set_nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),vAPP(sTfun(nat,$o),set_nat,collect_nat,X2))),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),vAPP(sTfun(nat,$o),set_nat,collect_nat,X3))) )
| ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,vAPP(set_nat,nat,vAPP(sTfun(nat,$o),sTfun(set_nat,nat),vAPP(sTfun(nat,$o),sTfun(sTfun(nat,$o),sTfun(set_nat,nat)),sK101,X3),X2),X0)),X0) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1560]) ).
thf(f1560,plain,
! [X0: set_nat,X1: set_nat,X2: nat > $o,X3: nat > $o] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),vAPP(sTfun(nat,$o),set_nat,collect_nat,X2))),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),vAPP(sTfun(nat,$o),set_nat,collect_nat,X3))) )
| ( ( $true != vAPP(nat,$o,X3,vAPP(set_nat,nat,vAPP(sTfun(nat,$o),sTfun(set_nat,nat),vAPP(sTfun(nat,$o),sTfun(sTfun(nat,$o),sTfun(set_nat,nat)),sK101,X3),X2),X0)) )
& ( $true = vAPP(nat,$o,X2,vAPP(set_nat,nat,vAPP(sTfun(nat,$o),sTfun(set_nat,nat),vAPP(sTfun(nat,$o),sTfun(sTfun(nat,$o),sTfun(set_nat,nat)),sK101,X3),X2),X0)) )
& ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,vAPP(set_nat,nat,vAPP(sTfun(nat,$o),sTfun(set_nat,nat),vAPP(sTfun(nat,$o),sTfun(sTfun(nat,$o),sTfun(set_nat,nat)),sK101,X3),X2),X0)),X0) ) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK101])],[f1348,f1559]) ).
thf(f1559,plain,
! [X0: set_nat,X2: nat > $o,X3: nat > $o] :
( ? [X4: nat] :
( ( $true != vAPP(nat,$o,X3,X4) )
& ( $true = vAPP(nat,$o,X2,X4) )
& ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X4),X0) ) )
=> ( ( $true != vAPP(nat,$o,X3,vAPP(set_nat,nat,vAPP(sTfun(nat,$o),sTfun(set_nat,nat),vAPP(sTfun(nat,$o),sTfun(sTfun(nat,$o),sTfun(set_nat,nat)),sK101,X3),X2),X0)) )
& ( $true = vAPP(nat,$o,X2,vAPP(set_nat,nat,vAPP(sTfun(nat,$o),sTfun(set_nat,nat),vAPP(sTfun(nat,$o),sTfun(sTfun(nat,$o),sTfun(set_nat,nat)),sK101,X3),X2),X0)) )
& ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,vAPP(set_nat,nat,vAPP(sTfun(nat,$o),sTfun(set_nat,nat),vAPP(sTfun(nat,$o),sTfun(sTfun(nat,$o),sTfun(set_nat,nat)),sK101,X3),X2),X0)),X0) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1348,plain,
! [X0: set_nat,X1: set_nat,X2: nat > $o,X3: nat > $o] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),vAPP(sTfun(nat,$o),set_nat,collect_nat,X2))),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),vAPP(sTfun(nat,$o),set_nat,collect_nat,X3))) )
| ? [X4: nat] :
( ( $true != vAPP(nat,$o,X3,X4) )
& ( $true = vAPP(nat,$o,X2,X4) )
& ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X4),X0) ) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1) ) ),
inference(flattening,[],[f1347]) ).
thf(f1347,plain,
! [X0: set_nat,X1: set_nat,X2: nat > $o,X3: nat > $o] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),vAPP(sTfun(nat,$o),set_nat,collect_nat,X2))),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),vAPP(sTfun(nat,$o),set_nat,collect_nat,X3))) )
| ? [X4: nat] :
( ( $true != vAPP(nat,$o,X3,X4) )
& ( $true = vAPP(nat,$o,X2,X4) )
& ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X4),X0) ) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1) ) ),
inference(ennf_transformation,[],[f929]) ).
thf(f929,plain,
! [X0: set_nat,X1: set_nat,X2: nat > $o,X3: nat > $o] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1) )
=> ( ! [X4: nat] :
( ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X4),X0) )
=> ( ( $true = vAPP(nat,$o,X2,X4) )
=> ( $true = vAPP(nat,$o,X3,X4) ) ) )
=> ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),vAPP(sTfun(nat,$o),set_nat,collect_nat,X2))),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),vAPP(sTfun(nat,$o),set_nat,collect_nat,X3))) ) ) ),
inference(fool_elimination,[],[f928]) ).
thf(f928,plain,
! [X0: set_nat,X1: set_nat,X2: nat > $o,X3: nat > $o] :
( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1)
=> ( ! [X4: nat] :
( vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X4),X0)
=> ( vAPP(nat,$o,X2,X4)
=> vAPP(nat,$o,X3,X4) ) )
=> vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),vAPP(sTfun(nat,$o),set_nat,collect_nat,X2))),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),vAPP(sTfun(nat,$o),set_nat,collect_nat,X3))) ) ),
inference(rectify,[],[f183]) ).
thf(f183,axiom,
! [X2: set_nat,X3: set_nat,X18: nat > $o,X27: nat > $o] :
( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X3)
=> ( ! [X4: nat] :
( vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X4),X2)
=> ( vAPP(nat,$o,X18,X4)
=> vAPP(nat,$o,X27,X4) ) )
=> vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X2),vAPP(sTfun(nat,$o),set_nat,collect_nat,X18))),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X3),vAPP(sTfun(nat,$o),set_nat,collect_nat,X27))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_Int__Collect__mono) ).
thf(f4911,plain,
( spl155_181
| ~ spl155_33
| ~ spl155_125 ),
inference(avatar_split_clause,[],[f3804,f3763,f2977,f4909]) ).
thf(f3804,plain,
( ! [X0: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),edges)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),X0) ) )
| ~ spl155_33
| ~ spl155_125 ),
inference(trivial_inequality_removal,[],[f3803]) ).
thf(f3803,plain,
( ! [X0: set_Pr1986765409at_nat] :
( ( $true != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),edges)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),X0) ) )
| ~ spl155_33
| ~ spl155_125 ),
inference(superposition,[],[f2978,f3765]) ).
thf(f4879,plain,
spl155_180,
inference(avatar_split_clause,[],[f2451,f4877]) ).
thf(f4877,plain,
( spl155_180
<=> ! [X0: set_Pr1986765409at_nat,X3: product_prod_nat_nat > $o,X2: product_prod_nat_nat > $o,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X2))),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X3))) )
| ( $true = vAPP(product_prod_nat_nat,$o,X2,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(sTfun(product_prod_nat_nat,$o),sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),vAPP(sTfun(product_prod_nat_nat,$o),sTfun(sTfun(product_prod_nat_nat,$o),sTfun(set_Pr1986765409at_nat,product_prod_nat_nat)),sK126,X3),X2),X0)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_180])]) ).
thf(f2451,plain,
! [X2: product_prod_nat_nat > $o,X3: product_prod_nat_nat > $o,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X2))),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X3))) )
| ( $true = vAPP(product_prod_nat_nat,$o,X2,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(sTfun(product_prod_nat_nat,$o),sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),vAPP(sTfun(product_prod_nat_nat,$o),sTfun(sTfun(product_prod_nat_nat,$o),sTfun(set_Pr1986765409at_nat,product_prod_nat_nat)),sK126,X3),X2),X0)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X1) ) ),
inference(definition_unfolding,[],[f2047,f1656,f1656]) ).
thf(f2047,plain,
! [X2: product_prod_nat_nat > $o,X3: product_prod_nat_nat > $o,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X2))),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X3))) )
| ( $true = vAPP(product_prod_nat_nat,$o,X2,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(sTfun(product_prod_nat_nat,$o),sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),vAPP(sTfun(product_prod_nat_nat,$o),sTfun(sTfun(product_prod_nat_nat,$o),sTfun(set_Pr1986765409at_nat,product_prod_nat_nat)),sK126,X3),X2),X0)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1586]) ).
thf(f4875,plain,
spl155_179,
inference(avatar_split_clause,[],[f2450,f4873]) ).
thf(f4873,plain,
( spl155_179
<=> ! [X0: set_Pr1986765409at_nat,X3: product_prod_nat_nat > $o,X2: product_prod_nat_nat > $o,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X2))),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X3))) )
| ( $true != vAPP(product_prod_nat_nat,$o,X3,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(sTfun(product_prod_nat_nat,$o),sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),vAPP(sTfun(product_prod_nat_nat,$o),sTfun(sTfun(product_prod_nat_nat,$o),sTfun(set_Pr1986765409at_nat,product_prod_nat_nat)),sK126,X3),X2),X0)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_179])]) ).
thf(f2450,plain,
! [X2: product_prod_nat_nat > $o,X3: product_prod_nat_nat > $o,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X2))),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X3))) )
| ( $true != vAPP(product_prod_nat_nat,$o,X3,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(sTfun(product_prod_nat_nat,$o),sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),vAPP(sTfun(product_prod_nat_nat,$o),sTfun(sTfun(product_prod_nat_nat,$o),sTfun(set_Pr1986765409at_nat,product_prod_nat_nat)),sK126,X3),X2),X0)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X1) ) ),
inference(definition_unfolding,[],[f2048,f1656,f1656]) ).
thf(f2048,plain,
! [X2: product_prod_nat_nat > $o,X3: product_prod_nat_nat > $o,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X2))),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X3))) )
| ( $true != vAPP(product_prod_nat_nat,$o,X3,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(sTfun(product_prod_nat_nat,$o),sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),vAPP(sTfun(product_prod_nat_nat,$o),sTfun(sTfun(product_prod_nat_nat,$o),sTfun(set_Pr1986765409at_nat,product_prod_nat_nat)),sK126,X3),X2),X0)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1586]) ).
thf(f4871,plain,
spl155_178,
inference(avatar_split_clause,[],[f2421,f4869]) ).
thf(f4869,plain,
( spl155_178
<=> ! [X0: set_nat,X3: nat > $o,X2: nat > $o,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),vAPP(sTfun(nat,$o),set_nat,collect_nat,X2))),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),vAPP(sTfun(nat,$o),set_nat,collect_nat,X3))) )
| ( $true = vAPP(nat,$o,X2,vAPP(set_nat,nat,vAPP(sTfun(nat,$o),sTfun(set_nat,nat),vAPP(sTfun(nat,$o),sTfun(sTfun(nat,$o),sTfun(set_nat,nat)),sK101,X3),X2),X0)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_178])]) ).
thf(f2421,plain,
! [X2: nat > $o,X3: nat > $o,X0: set_nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),vAPP(sTfun(nat,$o),set_nat,collect_nat,X2))),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),vAPP(sTfun(nat,$o),set_nat,collect_nat,X3))) )
| ( $true = vAPP(nat,$o,X2,vAPP(set_nat,nat,vAPP(sTfun(nat,$o),sTfun(set_nat,nat),vAPP(sTfun(nat,$o),sTfun(sTfun(nat,$o),sTfun(set_nat,nat)),sK101,X3),X2),X0)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),X1) ) ),
inference(definition_unfolding,[],[f2017,f1650,f1650]) ).
thf(f2017,plain,
! [X2: nat > $o,X3: nat > $o,X0: set_nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),vAPP(sTfun(nat,$o),set_nat,collect_nat,X2))),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),vAPP(sTfun(nat,$o),set_nat,collect_nat,X3))) )
| ( $true = vAPP(nat,$o,X2,vAPP(set_nat,nat,vAPP(sTfun(nat,$o),sTfun(set_nat,nat),vAPP(sTfun(nat,$o),sTfun(sTfun(nat,$o),sTfun(set_nat,nat)),sK101,X3),X2),X0)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1560]) ).
thf(f4867,plain,
spl155_177,
inference(avatar_split_clause,[],[f2420,f4865]) ).
thf(f4865,plain,
( spl155_177
<=> ! [X0: set_nat,X3: nat > $o,X2: nat > $o,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),vAPP(sTfun(nat,$o),set_nat,collect_nat,X2))),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),vAPP(sTfun(nat,$o),set_nat,collect_nat,X3))) )
| ( $true != vAPP(nat,$o,X3,vAPP(set_nat,nat,vAPP(sTfun(nat,$o),sTfun(set_nat,nat),vAPP(sTfun(nat,$o),sTfun(sTfun(nat,$o),sTfun(set_nat,nat)),sK101,X3),X2),X0)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_177])]) ).
thf(f2420,plain,
! [X2: nat > $o,X3: nat > $o,X0: set_nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),vAPP(sTfun(nat,$o),set_nat,collect_nat,X2))),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),vAPP(sTfun(nat,$o),set_nat,collect_nat,X3))) )
| ( $true != vAPP(nat,$o,X3,vAPP(set_nat,nat,vAPP(sTfun(nat,$o),sTfun(set_nat,nat),vAPP(sTfun(nat,$o),sTfun(sTfun(nat,$o),sTfun(set_nat,nat)),sK101,X3),X2),X0)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),X1) ) ),
inference(definition_unfolding,[],[f2018,f1650,f1650]) ).
thf(f2018,plain,
! [X2: nat > $o,X3: nat > $o,X0: set_nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),vAPP(sTfun(nat,$o),set_nat,collect_nat,X2))),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),vAPP(sTfun(nat,$o),set_nat,collect_nat,X3))) )
| ( $true != vAPP(nat,$o,X3,vAPP(set_nat,nat,vAPP(sTfun(nat,$o),sTfun(set_nat,nat),vAPP(sTfun(nat,$o),sTfun(sTfun(nat,$o),sTfun(set_nat,nat)),sK101,X3),X2),X0)) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1560]) ).
thf(f4855,plain,
spl155_176,
inference(avatar_split_clause,[],[f2335,f4853]) ).
thf(f4853,plain,
( spl155_176
<=> ! [X4: nat,X0: nat > $o,X2: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X4),vAPP(sTfun(nat,$o),nat,sK60,X0)) )
| ( $true != vAPP(nat,$o,X0,X4) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK61,X2),X0)),X2) )
| ( $true != vAPP(nat,$o,X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_176])]) ).
thf(f2335,plain,
! [X2: nat,X0: nat > $o,X1: nat,X4: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X4),vAPP(sTfun(nat,$o),nat,sK60,X0)) )
| ( $true != vAPP(nat,$o,X0,X4) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK61,X2),X0)),X2) )
| ( $true != vAPP(nat,$o,X0,X1) ) ),
inference(definition_unfolding,[],[f1903,f1646,f1646]) ).
thf(f1903,plain,
! [X2: nat,X0: nat > $o,X1: nat,X4: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),vAPP(sTfun(nat,$o),nat,sK60,X0)) )
| ( $true != vAPP(nat,$o,X0,X4) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK61,X2),X0)),X2) )
| ( $true != vAPP(nat,$o,X0,X1) ) ),
inference(cnf_transformation,[],[f1520]) ).
thf(f1520,plain,
! [X0: nat > $o,X1: nat,X2: nat] :
( ( ! [X4: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),vAPP(sTfun(nat,$o),nat,sK60,X0)) )
| ( $true != vAPP(nat,$o,X0,X4) ) )
& ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK60,X0)) ) )
| ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK61,X2),X0)),X2) )
& ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK61,X2),X0)) ) )
| ( $true != vAPP(nat,$o,X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK60,sK61])],[f1517,f1519,f1518]) ).
thf(f1518,plain,
! [X0: nat > $o] :
( ? [X3: nat] :
( ! [X4: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X3) )
| ( $true != vAPP(nat,$o,X0,X4) ) )
& ( $true = vAPP(nat,$o,X0,X3) ) )
=> ( ! [X4: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),vAPP(sTfun(nat,$o),nat,sK60,X0)) )
| ( $true != vAPP(nat,$o,X0,X4) ) )
& ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK60,X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1519,plain,
! [X0: nat > $o,X2: nat] :
( ? [X5: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X5),X2) )
& ( $true = vAPP(nat,$o,X0,X5) ) )
=> ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK61,X2),X0)),X2) )
& ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK61,X2),X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1517,plain,
! [X0: nat > $o,X1: nat,X2: nat] :
( ? [X3: nat] :
( ! [X4: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X3) )
| ( $true != vAPP(nat,$o,X0,X4) ) )
& ( $true = vAPP(nat,$o,X0,X3) ) )
| ? [X5: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X5),X2) )
& ( $true = vAPP(nat,$o,X0,X5) ) )
| ( $true != vAPP(nat,$o,X0,X1) ) ),
inference(rectify,[],[f1219]) ).
thf(f1219,plain,
! [X0: nat > $o,X1: nat,X2: nat] :
( ? [X4: nat] :
( ! [X5: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X5),X4) )
| ( $true != vAPP(nat,$o,X0,X5) ) )
& ( $true = vAPP(nat,$o,X0,X4) ) )
| ? [X3: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X2) )
& ( $true = vAPP(nat,$o,X0,X3) ) )
| ( $true != vAPP(nat,$o,X0,X1) ) ),
inference(flattening,[],[f1218]) ).
thf(f1218,plain,
! [X0: nat > $o,X1: nat,X2: nat] :
( ? [X4: nat] :
( ! [X5: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X5),X4) )
| ( $true != vAPP(nat,$o,X0,X5) ) )
& ( $true = vAPP(nat,$o,X0,X4) ) )
| ? [X3: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X2) )
& ( $true = vAPP(nat,$o,X0,X3) ) )
| ( $true != vAPP(nat,$o,X0,X1) ) ),
inference(ennf_transformation,[],[f769]) ).
thf(f769,plain,
! [X0: nat > $o,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
=> ( ! [X3: nat] :
( ( $true = vAPP(nat,$o,X0,X3) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X2) ) )
=> ~ ! [X4: nat] :
( ( $true = vAPP(nat,$o,X0,X4) )
=> ~ ! [X5: nat] :
( ( $true = vAPP(nat,$o,X0,X5) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X5),X4) ) ) ) ) ),
inference(fool_elimination,[],[f768]) ).
thf(f768,plain,
! [X0: nat > $o,X1: nat,X2: nat] :
( vAPP(nat,$o,X0,X1)
=> ( ! [X3: nat] :
( vAPP(nat,$o,X0,X3)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X2) )
=> ~ ! [X4: nat] :
( vAPP(nat,$o,X0,X4)
=> ~ ! [X5: nat] :
( vAPP(nat,$o,X0,X5)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X5),X4) ) ) ) ),
inference(rectify,[],[f346]) ).
thf(f346,axiom,
! [X18: nat > $o,X5: nat,X60: nat] :
( vAPP(nat,$o,X18,X5)
=> ( ! [X4: nat] :
( vAPP(nat,$o,X18,X4)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X60) )
=> ~ ! [X61: nat] :
( vAPP(nat,$o,X18,X61)
=> ~ ! [X62: nat] :
( vAPP(nat,$o,X18,X62)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X62),X61) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_345_bounded__Max__nat) ).
thf(f4834,plain,
spl155_175,
inference(avatar_split_clause,[],[f2221,f4832]) ).
thf(f2221,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( X0 = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0)),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X1),X0) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) ) ),
inference(definition_unfolding,[],[f1774,f1646,f1656]) ).
thf(f1774,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( X0 = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0)),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X1),X0) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) ) ),
inference(cnf_transformation,[],[f1129]) ).
thf(f1129,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( X0 = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0)),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X1),X0) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) ) ),
inference(flattening,[],[f1128]) ).
thf(f1128,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( X0 = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0)),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X1),X0) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) ) ),
inference(ennf_transformation,[],[f575]) ).
thf(f575,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) )
=> ( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X1),X0) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0)),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)) )
=> ( X0 = X1 ) ) ) ),
inference(fool_elimination,[],[f574]) ).
thf(f574,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0)
=> ( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X1),X0)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0)),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1))
=> ( X0 = X1 ) ) ) ),
inference(rectify,[],[f214]) ).
thf(f214,axiom,
! [X3: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat] :
( vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X3)
=> ( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X2),X3)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X3)),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X2))
=> ( X2 = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_card__seteq) ).
thf(f4788,plain,
spl155_174,
inference(avatar_split_clause,[],[f2223,f4786]) ).
thf(f2223,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X1),X0) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) ) ),
inference(definition_unfolding,[],[f1776,f1646,f1656]) ).
thf(f1776,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X1),X0) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) ) ),
inference(cnf_transformation,[],[f1133]) ).
thf(f1133,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X1),X0) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) ) ),
inference(flattening,[],[f1132]) ).
thf(f1132,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X1),X0) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) ) ),
inference(ennf_transformation,[],[f579]) ).
thf(f579,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) )
=> ( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X1),X0) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0)) ) ) ),
inference(fool_elimination,[],[f578]) ).
thf(f578,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0)
=> ( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X1),X0)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0)) ) ),
inference(rectify,[],[f212]) ).
thf(f212,axiom,
! [X3: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat] :
( vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X3)
=> ( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X2),X3)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X2)),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_card__mono) ).
thf(f4745,plain,
spl155_173,
inference(avatar_split_clause,[],[f2271,f4743]) ).
thf(f2271,plain,
! [X0: nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK28,X1),X0)),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)) ) ),
inference(definition_unfolding,[],[f1824,f1656,f1646]) ).
thf(f1824,plain,
! [X0: nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK28,X1),X0)),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)) ) ),
inference(cnf_transformation,[],[f1484]) ).
thf(f1484,plain,
! [X0: nat,X1: set_Pr1986765409at_nat] :
( ( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK28,X1),X0)) )
& ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK28,X1),X0)) = X0 )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK28,X1),X0)),X1) ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK28])],[f1196,f1483]) ).
thf(f1483,plain,
! [X0: nat,X1: set_Pr1986765409at_nat] :
( ? [X2: set_Pr1986765409at_nat] :
( ( vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X2) = $true )
& ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X2) = X0 )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X2),X1) ) )
=> ( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK28,X1),X0)) )
& ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK28,X1),X0)) = X0 )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK28,X1),X0)),X1) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1196,plain,
! [X0: nat,X1: set_Pr1986765409at_nat] :
( ? [X2: set_Pr1986765409at_nat] :
( ( vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X2) = $true )
& ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X2) = X0 )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X2),X1) ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)) ) ),
inference(flattening,[],[f1195]) ).
thf(f1195,plain,
! [X0: nat,X1: set_Pr1986765409at_nat] :
( ? [X2: set_Pr1986765409at_nat] :
( ( vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X2) = $true )
& ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X2) = X0 )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X2),X1) ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)) ) ),
inference(ennf_transformation,[],[f1048]) ).
thf(f1048,plain,
! [X0: nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)) )
=> ~ ! [X2: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X2),X1) )
=> ( ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X2) = X0 )
=> ( vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X2) != $true ) ) ) ),
inference(flattening,[],[f669]) ).
thf(f669,plain,
! [X0: nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)) )
=> ~ ! [X2: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X2),X1) )
=> ( ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X2) = X0 )
=> ( vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X2) != $true ) ) ) ),
inference(fool_elimination,[],[f668]) ).
thf(f668,plain,
! [X0: nat,X1: set_Pr1986765409at_nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1))
=> ~ ! [X2: set_Pr1986765409at_nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X2),X1)
=> ( ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X2) = X0 )
=> ~ vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X2) ) ) ),
inference(rectify,[],[f338]) ).
thf(f338,axiom,
! [X48: nat,X45: set_Pr1986765409at_nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X48),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X45))
=> ~ ! [X51: set_Pr1986765409at_nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X51),X45)
=> ( ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X51) = X48 )
=> ~ vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X51) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_337_obtain__subset__with__card__n) ).
thf(f4741,plain,
spl155_172,
inference(avatar_split_clause,[],[f2268,f4739]) ).
thf(f2268,plain,
! [X0: nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK27,X1),X0)),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),vAPP(set_nat,nat,finite_card_nat,X1)) ) ),
inference(definition_unfolding,[],[f1821,f1650,f1646]) ).
thf(f1821,plain,
! [X0: nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK27,X1),X0)),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(set_nat,nat,finite_card_nat,X1)) ) ),
inference(cnf_transformation,[],[f1482]) ).
thf(f4514,plain,
spl155_171,
inference(avatar_split_clause,[],[f2393,f4512]) ).
thf(f4512,plain,
( spl155_171
<=> ! [X2: set_Pr1986765409at_nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X1) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_171])]) ).
thf(f2393,plain,
! [X2: set_Pr1986765409at_nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X1) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),X2)) ) ),
inference(definition_unfolding,[],[f1968,f1656,f1656]) ).
thf(f1968,plain,
! [X2: set_Pr1986765409at_nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),X2)) ) ),
inference(cnf_transformation,[],[f1310]) ).
thf(f1310,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat] :
( ( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X2) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1) ) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),X2)) ) ),
inference(ennf_transformation,[],[f1058]) ).
thf(f1058,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),X2)) )
=> ~ ( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1) )
=> ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X2) ) ) ),
inference(flattening,[],[f887]) ).
thf(f887,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),X2)) )
=> ~ ( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1) )
=> ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X2) ) ) ),
inference(fool_elimination,[],[f886]) ).
thf(f886,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),X2))
=> ~ ( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1)
=> ~ vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X2) ) ),
inference(rectify,[],[f267]) ).
thf(f267,axiom,
! [X13: set_Pr1986765409at_nat,X12: set_Pr1986765409at_nat,X9: set_Pr1986765409at_nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X13),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X12),X9))
=> ~ ( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X13),X12)
=> ~ vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X13),X9) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_266_inf_OboundedE) ).
thf(f4510,plain,
spl155_170,
inference(avatar_split_clause,[],[f2392,f4508]) ).
thf(f4508,plain,
( spl155_170
<=> ! [X2: set_Pr1986765409at_nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X2) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_170])]) ).
thf(f2392,plain,
! [X2: set_Pr1986765409at_nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X2) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),X2)) ) ),
inference(definition_unfolding,[],[f1969,f1656,f1656]) ).
thf(f1969,plain,
! [X2: set_Pr1986765409at_nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X2) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),X2)) ) ),
inference(cnf_transformation,[],[f1310]) ).
thf(f4506,plain,
( spl155_169
| ~ spl155_6
| ~ spl155_154 ),
inference(avatar_split_clause,[],[f4459,f4321,f2785,f4503]) ).
thf(f4503,plain,
( spl155_169
<=> ( edges = vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,vAPP(set_Pr1986765409at_nat,list_P559422087at_nat,sK9,edges)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_169])]) ).
thf(f4459,plain,
( ( edges = vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,vAPP(set_Pr1986765409at_nat,list_P559422087at_nat,sK9,edges)) )
| ~ spl155_6
| ~ spl155_154 ),
inference(trivial_inequality_removal,[],[f4458]) ).
thf(f4458,plain,
( ( $true != $true )
| ( edges = vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,vAPP(set_Pr1986765409at_nat,list_P559422087at_nat,sK9,edges)) )
| ~ spl155_6
| ~ spl155_154 ),
inference(superposition,[],[f2786,f4323]) ).
thf(f4501,plain,
spl155_168,
inference(avatar_split_clause,[],[f2389,f4499]) ).
thf(f2389,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X1),X2)) ) ),
inference(definition_unfolding,[],[f1960,f1646,f1646]) ).
thf(f1960,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X1),X2)) ) ),
inference(cnf_transformation,[],[f1305]) ).
thf(f1305,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X1),X2)) ) ),
inference(ennf_transformation,[],[f1055]) ).
thf(f1055,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X1),X2)) )
=> ~ ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
=> ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) ) ) ),
inference(flattening,[],[f877]) ).
thf(f877,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X1),X2)) )
=> ~ ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
=> ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) ) ) ),
inference(fool_elimination,[],[f876]) ).
thf(f876,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X1),X2))
=> ~ ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1)
=> ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) ) ),
inference(rectify,[],[f269]) ).
thf(f269,axiom,
! [X13: nat,X12: nat,X9: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X13),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X12),X9))
=> ~ ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X13),X12)
=> ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X13),X9) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_268_inf_OboundedE) ).
thf(f4497,plain,
spl155_167,
inference(avatar_split_clause,[],[f2388,f4495]) ).
thf(f2388,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X1),X2)) ) ),
inference(definition_unfolding,[],[f1961,f1646,f1646]) ).
thf(f1961,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X1),X2)) ) ),
inference(cnf_transformation,[],[f1305]) ).
thf(f4493,plain,
spl155_166,
inference(avatar_split_clause,[],[f2385,f4491]) ).
thf(f4491,plain,
( spl155_166
<=> ! [X2: set_nat,X0: set_nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),X1) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_166])]) ).
thf(f2385,plain,
! [X2: set_nat,X0: set_nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),X1) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),X2)) ) ),
inference(definition_unfolding,[],[f1952,f1650,f1650]) ).
thf(f1952,plain,
! [X2: set_nat,X0: set_nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),X2)) ) ),
inference(cnf_transformation,[],[f1300]) ).
thf(f1300,plain,
! [X0: set_nat,X1: set_nat,X2: set_nat] :
( ( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X2) )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1) ) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),X2)) ) ),
inference(ennf_transformation,[],[f1052]) ).
thf(f1052,plain,
! [X0: set_nat,X1: set_nat,X2: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),X2)) )
=> ~ ( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1) )
=> ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X2) ) ) ),
inference(flattening,[],[f867]) ).
thf(f867,plain,
! [X0: set_nat,X1: set_nat,X2: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),X2)) )
=> ~ ( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1) )
=> ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X2) ) ) ),
inference(fool_elimination,[],[f866]) ).
thf(f866,plain,
! [X0: set_nat,X1: set_nat,X2: set_nat] :
( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),X2))
=> ~ ( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1)
=> ~ vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X2) ) ),
inference(rectify,[],[f268]) ).
thf(f268,axiom,
! [X13: set_nat,X12: set_nat,X9: set_nat] :
( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X13),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X12),X9))
=> ~ ( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X13),X12)
=> ~ vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X13),X9) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_267_inf_OboundedE) ).
thf(f4489,plain,
spl155_165,
inference(avatar_split_clause,[],[f2384,f4487]) ).
thf(f4487,plain,
( spl155_165
<=> ! [X2: set_nat,X0: set_nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),X2) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_165])]) ).
thf(f2384,plain,
! [X2: set_nat,X0: set_nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),X2) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),X2)) ) ),
inference(definition_unfolding,[],[f1953,f1650,f1650]) ).
thf(f1953,plain,
! [X2: set_nat,X0: set_nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X2) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),X2)) ) ),
inference(cnf_transformation,[],[f1300]) ).
thf(f4485,plain,
spl155_164,
inference(avatar_split_clause,[],[f2379,f4483]) ).
thf(f2379,plain,
! [X2: set_Pr1986765409at_nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X2),X0)),X1) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X1) ) ),
inference(definition_unfolding,[],[f1947,f1656,f1656]) ).
thf(f1947,plain,
! [X2: set_Pr1986765409at_nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X2),X0)),X1) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1294]) ).
thf(f1294,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X2),X0)),X1) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1) ) ),
inference(ennf_transformation,[],[f857]) ).
thf(f857,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1) )
=> ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X2),X0)),X1) ) ),
inference(fool_elimination,[],[f856]) ).
thf(f856,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1)
=> vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X2),X0)),X1) ),
inference(rectify,[],[f294]) ).
thf(f294,axiom,
! [X12: set_Pr1986765409at_nat,X5: set_Pr1986765409at_nat,X13: set_Pr1986765409at_nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X12),X5)
=> vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X13),X12)),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_293_le__infI2) ).
thf(f4481,plain,
spl155_163,
inference(avatar_split_clause,[],[f2378,f4479]) ).
thf(f2378,plain,
! [X2: set_Pr1986765409at_nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X2)),X1) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X1) ) ),
inference(definition_unfolding,[],[f1946,f1656,f1656]) ).
thf(f1946,plain,
! [X2: set_Pr1986765409at_nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X2)),X1) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1293]) ).
thf(f1293,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X2)),X1) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1) ) ),
inference(ennf_transformation,[],[f855]) ).
thf(f855,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1) )
=> ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X2)),X1) ) ),
inference(fool_elimination,[],[f854]) ).
thf(f854,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1)
=> vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X2)),X1) ),
inference(rectify,[],[f243]) ).
thf(f243,axiom,
! [X13: set_Pr1986765409at_nat,X9: set_Pr1986765409at_nat,X12: set_Pr1986765409at_nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X13),X9)
=> vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X13),X12)),X9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_inf_OcoboundedI1) ).
thf(f4477,plain,
spl155_162,
inference(avatar_split_clause,[],[f2364,f4475]) ).
thf(f2364,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X2)),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),X1) ) ),
inference(definition_unfolding,[],[f1931,f1646,f1646]) ).
thf(f1931,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X2)),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1266]) ).
thf(f1266,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X2)),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(ennf_transformation,[],[f825]) ).
thf(f825,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X2)),X1) ) ),
inference(fool_elimination,[],[f824]) ).
thf(f824,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X2)),X1) ),
inference(rectify,[],[f245]) ).
thf(f245,axiom,
! [X13: nat,X9: nat,X12: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X13),X9)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X13),X12)),X9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_inf_OcoboundedI1) ).
thf(f4473,plain,
spl155_161,
inference(avatar_split_clause,[],[f2363,f4471]) ).
thf(f2363,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X2),X0)),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),X1) ) ),
inference(definition_unfolding,[],[f1930,f1646,f1646]) ).
thf(f1930,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X2),X0)),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1265]) ).
thf(f1265,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X2),X0)),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(ennf_transformation,[],[f823]) ).
thf(f823,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X2),X0)),X1) ) ),
inference(fool_elimination,[],[f822]) ).
thf(f822,plain,
! [X0: nat,X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X2),X0)),X1) ),
inference(rectify,[],[f242]) ).
thf(f242,axiom,
! [X12: nat,X9: nat,X13: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X12),X9)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X13),X12)),X9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_inf_OcoboundedI2) ).
thf(f4469,plain,
spl155_160,
inference(avatar_split_clause,[],[f2353,f4467]) ).
thf(f2353,plain,
! [X2: set_nat,X0: set_nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X2)),X1) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),X1) ) ),
inference(definition_unfolding,[],[f1919,f1650,f1650]) ).
thf(f1919,plain,
! [X2: set_nat,X0: set_nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X2)),X1) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1246]) ).
thf(f1246,plain,
! [X0: set_nat,X1: set_nat,X2: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X2)),X1) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1) ) ),
inference(ennf_transformation,[],[f801]) ).
thf(f801,plain,
! [X0: set_nat,X1: set_nat,X2: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1) )
=> ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X2)),X1) ) ),
inference(fool_elimination,[],[f800]) ).
thf(f800,plain,
! [X0: set_nat,X1: set_nat,X2: set_nat] :
( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1)
=> vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X2)),X1) ),
inference(rectify,[],[f298]) ).
thf(f298,axiom,
! [X13: set_nat,X5: set_nat,X12: set_nat] :
( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X13),X5)
=> vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X13),X12)),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_297_le__infI1) ).
thf(f4465,plain,
spl155_159,
inference(avatar_split_clause,[],[f2352,f4463]) ).
thf(f2352,plain,
! [X2: set_nat,X0: set_nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X2),X0)),X1) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),X1) ) ),
inference(definition_unfolding,[],[f1918,f1650,f1650]) ).
thf(f1918,plain,
! [X2: set_nat,X0: set_nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X2),X0)),X1) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1245]) ).
thf(f1245,plain,
! [X0: set_nat,X1: set_nat,X2: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X2),X0)),X1) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1) ) ),
inference(ennf_transformation,[],[f799]) ).
thf(f799,plain,
! [X0: set_nat,X1: set_nat,X2: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1) )
=> ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X2),X0)),X1) ) ),
inference(fool_elimination,[],[f798]) ).
thf(f798,plain,
! [X0: set_nat,X1: set_nat,X2: set_nat] :
( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1)
=> vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X2),X0)),X1) ),
inference(rectify,[],[f295]) ).
thf(f295,axiom,
! [X12: set_nat,X5: set_nat,X13: set_nat] :
( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X12),X5)
=> vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X13),X12)),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_294_le__infI2) ).
thf(f4396,plain,
spl155_158,
inference(avatar_split_clause,[],[f2262,f4394]) ).
thf(f2262,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( X0 = X1 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X1),X0) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X1) ) ),
inference(definition_unfolding,[],[f1815,f1656,f1656]) ).
thf(f1815,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( X0 = X1 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X1),X0) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1184]) ).
thf(f1184,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( X0 = X1 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X1),X0) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1) ) ),
inference(flattening,[],[f1183]) ).
thf(f1183,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( X0 = X1 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X1),X0) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1) ) ),
inference(ennf_transformation,[],[f657]) ).
thf(f657,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1) )
=> ( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X1),X0) )
=> ( X0 = X1 ) ) ),
inference(fool_elimination,[],[f656]) ).
thf(f656,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1)
=> ( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X1),X0)
=> ( X0 = X1 ) ) ),
inference(rectify,[],[f69]) ).
thf(f69,axiom,
! [X5: set_Pr1986765409at_nat,X21: set_Pr1986765409at_nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X5),X21)
=> ( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X21),X5)
=> ( X5 = X21 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_antisym) ).
thf(f4392,plain,
spl155_157,
inference(avatar_split_clause,[],[f2249,f4390]) ).
thf(f2249,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X1),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),X1) ) ),
inference(definition_unfolding,[],[f1802,f1646,f1646]) ).
thf(f1802,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1166]) ).
thf(f1166,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(flattening,[],[f1165]) ).
thf(f1165,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(ennf_transformation,[],[f631]) ).
thf(f631,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) )
=> ( X0 = X1 ) ) ),
inference(fool_elimination,[],[f630]) ).
thf(f630,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0)
=> ( X0 = X1 ) ) ),
inference(rectify,[],[f71]) ).
thf(f71,axiom,
! [X5: nat,X21: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X5),X21)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X21),X5)
=> ( X5 = X21 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_antisym) ).
thf(f4388,plain,
spl155_156,
inference(avatar_split_clause,[],[f2239,f4386]) ).
thf(f2239,plain,
! [X0: set_nat,X1: set_nat] :
( ( X0 = X1 )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X1),X0) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),X1) ) ),
inference(definition_unfolding,[],[f1792,f1650,f1650]) ).
thf(f1792,plain,
! [X0: set_nat,X1: set_nat] :
( ( X0 = X1 )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X1),X0) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1152]) ).
thf(f1152,plain,
! [X0: set_nat,X1: set_nat] :
( ( X0 = X1 )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X1),X0) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1) ) ),
inference(flattening,[],[f1151]) ).
thf(f1151,plain,
! [X0: set_nat,X1: set_nat] :
( ( X0 = X1 )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X1),X0) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1) ) ),
inference(ennf_transformation,[],[f611]) ).
thf(f611,plain,
! [X0: set_nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1) )
=> ( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X1),X0) )
=> ( X0 = X1 ) ) ),
inference(fool_elimination,[],[f610]) ).
thf(f610,plain,
! [X0: set_nat,X1: set_nat] :
( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1)
=> ( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X1),X0)
=> ( X0 = X1 ) ) ),
inference(rectify,[],[f30]) ).
thf(f30,axiom,
! [X12: set_nat,X13: set_nat] :
( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X12),X13)
=> ( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X13),X12)
=> ( X12 = X13 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_dual__order_Oantisym) ).
thf(f4328,plain,
spl155_155,
inference(avatar_split_clause,[],[f2164,f4326]) ).
thf(f2164,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X1),X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),X1) ) ),
inference(definition_unfolding,[],[f1707,f1646,f1646]) ).
thf(f1707,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f505]) ).
thf(f505,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(fool_elimination,[],[f504]) ).
thf(f504,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0)
| vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ),
inference(rectify,[],[f68]) ).
thf(f68,axiom,
! [X5: nat,X21: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X21),X5)
| vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X5),X21) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_linear) ).
thf(f4324,plain,
( spl155_154
| ~ spl155_30
| ~ spl155_138 ),
inference(avatar_split_clause,[],[f4196,f3848,f2958,f4321]) ).
thf(f2958,plain,
( spl155_30
<=> ! [X0: list_P559422087at_nat,X1: set_Pr1986765409at_nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X0)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_30])]) ).
thf(f3848,plain,
( spl155_138
<=> ( edges = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p)),edges) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_138])]) ).
thf(f4196,plain,
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,edges) )
| ~ spl155_30
| ~ spl155_138 ),
inference(superposition,[],[f2959,f3850]) ).
thf(f3850,plain,
( ( edges = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p)),edges) )
| ~ spl155_138 ),
inference(avatar_component_clause,[],[f3848]) ).
thf(f2959,plain,
( ! [X0: list_P559422087at_nat,X1: set_Pr1986765409at_nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X0)),X1)) )
| ~ spl155_30 ),
inference(avatar_component_clause,[],[f2958]) ).
thf(f4319,plain,
spl155_153,
inference(avatar_split_clause,[],[f2123,f4316]) ).
thf(f4316,plain,
( spl155_153
<=> ( vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB) = vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),cCOMB,inf_in586391887at_nat)))),iCOMB) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_153])]) ).
thf(f2123,plain,
vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB) = vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),cCOMB,inf_in586391887at_nat)))),iCOMB),
inference(definition_unfolding,[],[f1659,f1656]) ).
thf(f1659,plain,
ord_le841296385at_nat = vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),cCOMB,inf_in586391887at_nat)))),iCOMB),
inference(cnf_transformation,[],[f413]) ).
thf(f413,plain,
ord_le841296385at_nat = vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),cCOMB,inf_in586391887at_nat)))),iCOMB),
inference(fool_elimination,[],[f412]) ).
thf(f412,plain,
( ord_le841296385at_nat
= ( ^ [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] : ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),X0) = X0 ) ) ),
inference(rectify,[],[f246]) ).
thf(f246,axiom,
( ord_le841296385at_nat
= ( ^ [X17: set_Pr1986765409at_nat,X16: set_Pr1986765409at_nat] : ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X16),X17) = X17 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_inf_Oabsorb__iff2) ).
thf(f4314,plain,
spl155_152,
inference(avatar_split_clause,[],[f2118,f4311]) ).
thf(f4311,plain,
( spl155_152
<=> ( vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB) = vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,set_nat)),cCOMB,inf_inf_set_nat)))),iCOMB) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_152])]) ).
thf(f2118,plain,
vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB) = vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,set_nat)),cCOMB,inf_inf_set_nat)))),iCOMB),
inference(definition_unfolding,[],[f1653,f1650]) ).
thf(f1653,plain,
ord_less_eq_set_nat = vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,set_nat)),cCOMB,inf_inf_set_nat)))),iCOMB),
inference(cnf_transformation,[],[f401]) ).
thf(f401,plain,
ord_less_eq_set_nat = vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,set_nat)),cCOMB,inf_inf_set_nat)))),iCOMB),
inference(fool_elimination,[],[f400]) ).
thf(f400,plain,
( ord_less_eq_set_nat
= ( ^ [X0: set_nat,X1: set_nat] : ( vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),X0) = X0 ) ) ),
inference(rectify,[],[f247]) ).
thf(f247,axiom,
( ord_less_eq_set_nat
= ( ^ [X17: set_nat,X16: set_nat] : ( vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X16),X17) = X17 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_inf_Oabsorb__iff2) ).
thf(f4309,plain,
spl155_151,
inference(avatar_split_clause,[],[f2114,f4306]) ).
thf(f4306,plain,
( spl155_151
<=> ( vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB) = vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,nat)),cCOMB,inf_inf_nat)))),iCOMB) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_151])]) ).
thf(f2114,plain,
vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB) = vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,nat)),cCOMB,inf_inf_nat)))),iCOMB),
inference(definition_unfolding,[],[f1648,f1646]) ).
thf(f1648,plain,
ord_less_eq_nat = vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,nat)),cCOMB,inf_inf_nat)))),iCOMB),
inference(cnf_transformation,[],[f391]) ).
thf(f391,plain,
ord_less_eq_nat = vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,nat)),cCOMB,inf_inf_nat)))),iCOMB),
inference(fool_elimination,[],[f390]) ).
thf(f390,plain,
( ord_less_eq_nat
= ( ^ [X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X1),X0) = X0 ) ) ),
inference(rectify,[],[f248]) ).
thf(f248,axiom,
( ord_less_eq_nat
= ( ^ [X17: nat,X16: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X16),X17) = X17 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_inf_Oabsorb__iff2) ).
thf(f4296,plain,
spl155_150,
inference(avatar_split_clause,[],[f2480,f4294]) ).
thf(f2480,plain,
! [X2: product_prod_nat_nat > a,X3: nat,X0: list_P559422087at_nat,X1: product_prod_nat_nat > a,X4: nat] :
( ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,X2),X3),X0),X4) )
| ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,X1),X3),X0),X4) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X0)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X1))),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X2)) ) ),
inference(definition_unfolding,[],[f2083,f1656]) ).
thf(f2083,plain,
! [X2: product_prod_nat_nat > a,X3: nat,X0: list_P559422087at_nat,X1: product_prod_nat_nat > a,X4: nat] :
( ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,X2),X3),X0),X4) )
| ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,X1),X3),X0),X4) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X0)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X1))),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X2)) ) ),
inference(cnf_transformation,[],[f1423]) ).
thf(f1423,plain,
! [X0: list_P559422087at_nat,X1: product_prod_nat_nat > a,X2: product_prod_nat_nat > a,X3: nat,X4: nat] :
( ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,X2),X3),X0),X4) )
| ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,X1),X3),X0),X4) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X0)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X1))),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X2)) ) ),
inference(flattening,[],[f1422]) ).
thf(f1422,plain,
! [X0: list_P559422087at_nat,X1: product_prod_nat_nat > a,X2: product_prod_nat_nat > a,X3: nat,X4: nat] :
( ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,X2),X3),X0),X4) )
| ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,X1),X3),X0),X4) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X0)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X1))),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X2)) ) ),
inference(ennf_transformation,[],[f1007]) ).
thf(f1007,plain,
! [X0: list_P559422087at_nat,X1: product_prod_nat_nat > a,X2: product_prod_nat_nat > a,X3: nat,X4: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X0)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X1))),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X2)) )
=> ( ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,X1),X3),X0),X4) )
=> ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,X2),X3),X0),X4) ) ) ),
inference(fool_elimination,[],[f1006]) ).
thf(f1006,plain,
! [X0: list_P559422087at_nat,X1: product_prod_nat_nat > a,X2: product_prod_nat_nat > a,X3: nat,X4: nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X0)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X1))),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X2))
=> ( vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,X1),X3),X0),X4)
=> vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,X2),X3),X0),X4) ) ),
inference(rectify,[],[f191]) ).
thf(f191,axiom,
! [X6: list_P559422087at_nat,X9: product_prod_nat_nat > a,X32: product_prod_nat_nat > a,X1: nat,X7: nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X6)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X9))),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X32))
=> ( vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,X9),X1),X6),X7)
=> vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,X32),X1),X6),X7) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_Graph_Otransfer__path) ).
thf(f4214,plain,
spl155_149,
inference(avatar_split_clause,[],[f2635,f4212]) ).
thf(f2635,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X2),X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP5,X2),X1),X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP4,X0),X2),X1) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP3,X1),X0),X2) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP2,X0),X1),X2) ) ),
inference(duplicate_literal_removal,[],[f2322]) ).
thf(f2322,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X2),X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X2),X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP5,X2),X1),X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP4,X0),X2),X1) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP3,X1),X0),X2) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP2,X0),X1),X2) ) ),
inference(definition_unfolding,[],[f1880,f1646,f1646]) ).
thf(f1880,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP5,X2),X1),X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP4,X0),X2),X1) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP3,X1),X0),X2) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP2,X0),X1),X2) ) ),
inference(cnf_transformation,[],[f1436]) ).
thf(f4206,plain,
spl155_148,
inference(avatar_split_clause,[],[f2382,f4204]) ).
thf(f4204,plain,
( spl155_148
<=> ! [X2: nat,X0: nat,X1: list_P559422087at_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(list_nat,set_nat,set_nat2,vAPP(list_P559422087at_nat,list_nat,vAPP(nat,sTfun(list_P559422087at_nat,list_nat),pathVertices,X0),X1))),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,c)) )
| ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2) )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,c)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_148])]) ).
thf(f2382,plain,
! [X2: nat,X0: nat,X1: list_P559422087at_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(list_nat,set_nat,set_nat2,vAPP(list_P559422087at_nat,list_nat,vAPP(nat,sTfun(list_P559422087at_nat,list_nat),pathVertices,X0),X1))),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,c)) )
| ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2) )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,c)) ) ),
inference(definition_unfolding,[],[f1950,f1650]) ).
thf(f1950,plain,
! [X2: nat,X0: nat,X1: list_P559422087at_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(list_nat,set_nat,set_nat2,vAPP(list_P559422087at_nat,list_nat,vAPP(nat,sTfun(list_P559422087at_nat,list_nat),pathVertices,X0),X1))),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,c)) )
| ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2) )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,c)) ) ),
inference(cnf_transformation,[],[f1298]) ).
thf(f1298,plain,
! [X0: nat,X1: list_P559422087at_nat,X2: nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(list_nat,set_nat,set_nat2,vAPP(list_P559422087at_nat,list_nat,vAPP(nat,sTfun(list_P559422087at_nat,list_nat),pathVertices,X0),X1))),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,c)) )
| ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2) )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,c)) ) ),
inference(flattening,[],[f1297]) ).
thf(f1297,plain,
! [X0: nat,X1: list_P559422087at_nat,X2: nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(list_nat,set_nat,set_nat2,vAPP(list_P559422087at_nat,list_nat,vAPP(nat,sTfun(list_P559422087at_nat,list_nat),pathVertices,X0),X1))),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,c)) )
| ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2) )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,c)) ) ),
inference(ennf_transformation,[],[f863]) ).
thf(f863,plain,
! [X0: nat,X1: list_P559422087at_nat,X2: nat] :
( ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,c)) )
=> ( ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2) )
=> ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(list_nat,set_nat,set_nat2,vAPP(list_P559422087at_nat,list_nat,vAPP(nat,sTfun(list_P559422087at_nat,list_nat),pathVertices,X0),X1))),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,c)) ) ) ),
inference(fool_elimination,[],[f862]) ).
thf(f862,plain,
! [X0: nat,X1: list_P559422087at_nat,X2: nat] :
( vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,c))
=> ( vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2)
=> vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(list_nat,set_nat,set_nat2,vAPP(list_P559422087at_nat,list_nat,vAPP(nat,sTfun(list_P559422087at_nat,list_nat),pathVertices,X0),X1))),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,c)) ) ),
inference(rectify,[],[f337]) ).
thf(f337,axiom,
! [X1: nat,X6: list_P559422087at_nat,X7: nat] :
( vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X1),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,c))
=> ( vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X1),X6),X7)
=> vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(list_nat,set_nat,set_nat2,vAPP(list_P559422087at_nat,list_nat,vAPP(nat,sTfun(list_P559422087at_nat,list_nat),pathVertices,X1),X6))),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,c)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_336_pathVertices__edgeset) ).
thf(f4067,plain,
spl155_147,
inference(avatar_split_clause,[],[f2325,f4065]) ).
thf(f2325,plain,
! [X2: nat,X0: nat > nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK36,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,X0)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK37,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK38,X0)) ) ),
inference(definition_unfolding,[],[f1887,f1646]) ).
thf(f1887,plain,
! [X2: nat,X0: nat > nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK36,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,X0)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK37,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK38,X0)) ) ),
inference(cnf_transformation,[],[f1501]) ).
thf(f1501,plain,
! [X0: nat > nat > $o,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2) )
| ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK36,X0)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK36,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,X0)) ) )
| ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK37,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK38,X0)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK37,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK38,X0)) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK35,sK36,sK37,sK38])],[f1498,f1500,f1499]) ).
thf(f1499,plain,
! [X0: nat > nat > $o] :
( ? [X3: nat,X4: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X3),X4) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X4),X3) ) )
=> ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK36,X0)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK36,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1500,plain,
! [X0: nat > nat > $o] :
( ? [X5: nat,X6: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X5),X6) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X5),X6) ) )
=> ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK37,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK38,X0)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK37,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK38,X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1498,plain,
! [X0: nat > nat > $o,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2) )
| ? [X3: nat,X4: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X3),X4) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X4),X3) ) )
| ? [X5: nat,X6: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X5),X6) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X5),X6) ) ) ),
inference(rectify,[],[f1211]) ).
thf(f1211,plain,
! [X0: nat > nat > $o,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2) )
| ? [X5: nat,X6: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X5),X6) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X6),X5) ) )
| ? [X3: nat,X4: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X3),X4) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X4) ) ) ),
inference(flattening,[],[f1210]) ).
thf(f1210,plain,
! [X0: nat > nat > $o,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2) )
| ? [X5: nat,X6: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X5),X6) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X6),X5) ) )
| ? [X3: nat,X4: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X3),X4) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X4) ) ) ),
inference(ennf_transformation,[],[f761]) ).
thf(f761,plain,
! [X0: nat > nat > $o,X1: nat,X2: nat] :
( ! [X3: nat,X4: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X4) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X3),X4) ) )
=> ( ! [X5: nat,X6: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X6),X5) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X5),X6) ) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2) ) ) ),
inference(fool_elimination,[],[f760]) ).
thf(f760,plain,
! [X0: nat > nat > $o,X1: nat,X2: nat] :
( ! [X3: nat,X4: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X4)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X3),X4) )
=> ( ! [X5: nat,X6: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X6),X5)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X5),X6) )
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2) ) ),
inference(rectify,[],[f38]) ).
thf(f38,axiom,
! [X18: nat > nat > $o,X13: nat,X12: nat] :
( ! [X19: nat,X20: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X19),X20)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X18,X19),X20) )
=> ( ! [X19: nat,X20: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X18,X20),X19)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X18,X19),X20) )
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X18,X13),X12) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_linorder__wlog) ).
thf(f4063,plain,
spl155_146,
inference(avatar_split_clause,[],[f2324,f4061]) ).
thf(f4061,plain,
( spl155_146
<=> ! [X2: nat,X0: nat > nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK36,X0)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK37,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK38,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_146])]) ).
thf(f2324,plain,
! [X2: nat,X0: nat > nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK36,X0)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK37,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK38,X0)) ) ),
inference(definition_unfolding,[],[f1889,f1646]) ).
thf(f1889,plain,
! [X2: nat,X0: nat > nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK36,X0)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK37,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK38,X0)) ) ),
inference(cnf_transformation,[],[f1501]) ).
thf(f4029,plain,
spl155_145,
inference(avatar_split_clause,[],[f2208,f4027]) ).
thf(f2208,plain,
! [X3: set_Pr1986765409at_nat,X0: set_se1612935105at_nat,X1: set_Pr1986765409at_nat] :
( ( vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK21,X1),X0) = X3 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK21,X1),X0)),X3) )
| ( $true != vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X3),X0) )
| ( $true != vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X1),X0) )
| ( $true != vAPP(set_se1612935105at_nat,$o,finite1457549322at_nat,X0) ) ),
inference(definition_unfolding,[],[f1762,f1656]) ).
thf(f1762,plain,
! [X3: set_Pr1986765409at_nat,X0: set_se1612935105at_nat,X1: set_Pr1986765409at_nat] :
( ( vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK21,X1),X0) = X3 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK21,X1),X0)),X3) )
| ( $true != vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X3),X0) )
| ( $true != vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X1),X0) )
| ( $true != vAPP(set_se1612935105at_nat,$o,finite1457549322at_nat,X0) ) ),
inference(cnf_transformation,[],[f1472]) ).
thf(f1472,plain,
! [X0: set_se1612935105at_nat,X1: set_Pr1986765409at_nat] :
( ( ! [X3: set_Pr1986765409at_nat] :
( ( vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK21,X1),X0) = X3 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK21,X1),X0)),X3) )
| ( $true != vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X3),X0) ) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X1),vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK21,X1),X0)) )
& ( $true = vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK21,X1),X0)),X0) ) )
| ( $true != vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X1),X0) )
| ( $true != vAPP(set_se1612935105at_nat,$o,finite1457549322at_nat,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK21])],[f1113,f1471]) ).
thf(f1471,plain,
! [X0: set_se1612935105at_nat,X1: set_Pr1986765409at_nat] :
( ? [X2: set_Pr1986765409at_nat] :
( ! [X3: set_Pr1986765409at_nat] :
( ( X2 = X3 )
| ( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X2),X3) != $true )
| ( $true != vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X3),X0) ) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X1),X2) )
& ( $true = vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X2),X0) ) )
=> ( ! [X3: set_Pr1986765409at_nat] :
( ( vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK21,X1),X0) = X3 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK21,X1),X0)),X3) )
| ( $true != vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X3),X0) ) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X1),vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK21,X1),X0)) )
& ( $true = vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK21,X1),X0)),X0) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1113,plain,
! [X0: set_se1612935105at_nat,X1: set_Pr1986765409at_nat] :
( ? [X2: set_Pr1986765409at_nat] :
( ! [X3: set_Pr1986765409at_nat] :
( ( X2 = X3 )
| ( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X2),X3) != $true )
| ( $true != vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X3),X0) ) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X1),X2) )
& ( $true = vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X2),X0) ) )
| ( $true != vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X1),X0) )
| ( $true != vAPP(set_se1612935105at_nat,$o,finite1457549322at_nat,X0) ) ),
inference(flattening,[],[f1112]) ).
thf(f1112,plain,
! [X0: set_se1612935105at_nat,X1: set_Pr1986765409at_nat] :
( ? [X2: set_Pr1986765409at_nat] :
( ! [X3: set_Pr1986765409at_nat] :
( ( X2 = X3 )
| ( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X2),X3) != $true )
| ( $true != vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X3),X0) ) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X1),X2) )
& ( $true = vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X2),X0) ) )
| ( $true != vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X1),X0) )
| ( $true != vAPP(set_se1612935105at_nat,$o,finite1457549322at_nat,X0) ) ),
inference(ennf_transformation,[],[f559]) ).
thf(f559,plain,
! [X0: set_se1612935105at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_se1612935105at_nat,$o,finite1457549322at_nat,X0) )
=> ( ( $true = vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X1),X0) )
=> ? [X2: set_Pr1986765409at_nat] :
( ! [X3: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X3),X0) )
=> ( ( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X2),X3) = $true )
=> ( X2 = X3 ) ) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X1),X2) )
& ( $true = vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X2),X0) ) ) ) ),
inference(fool_elimination,[],[f558]) ).
thf(f558,plain,
! [X0: set_se1612935105at_nat,X1: set_Pr1986765409at_nat] :
( vAPP(set_se1612935105at_nat,$o,finite1457549322at_nat,X0)
=> ( vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X1),X0)
=> ? [X2: set_Pr1986765409at_nat] :
( ! [X3: set_Pr1986765409at_nat] :
( vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X3),X0)
=> ( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X2),X3)
=> ( X2 = X3 ) ) )
& vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X1),X2)
& vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X2),X0) ) ) ),
inference(rectify,[],[f237]) ).
thf(f237,axiom,
! [X2: set_se1612935105at_nat,X13: set_Pr1986765409at_nat] :
( vAPP(set_se1612935105at_nat,$o,finite1457549322at_nat,X2)
=> ( vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X13),X2)
=> ? [X4: set_Pr1986765409at_nat] :
( ! [X42: set_Pr1986765409at_nat] :
( vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X42),X2)
=> ( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X4),X42)
=> ( X4 = X42 ) ) )
& vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X13),X4)
& vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X4),X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_finite__has__maximal2) ).
thf(f4025,plain,
spl155_144,
inference(avatar_split_clause,[],[f2206,f4023]) ).
thf(f2206,plain,
! [X3: set_Pr1986765409at_nat,X0: set_se1612935105at_nat,X1: set_Pr1986765409at_nat] :
( ( vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK20,X1),X0) = X3 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X3),vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK20,X1),X0)) )
| ( $true != vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X3),X0) )
| ( $true != vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X1),X0) )
| ( $true != vAPP(set_se1612935105at_nat,$o,finite1457549322at_nat,X0) ) ),
inference(definition_unfolding,[],[f1759,f1656]) ).
thf(f1759,plain,
! [X3: set_Pr1986765409at_nat,X0: set_se1612935105at_nat,X1: set_Pr1986765409at_nat] :
( ( vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK20,X1),X0) = X3 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X3),vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK20,X1),X0)) )
| ( $true != vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X3),X0) )
| ( $true != vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X1),X0) )
| ( $true != vAPP(set_se1612935105at_nat,$o,finite1457549322at_nat,X0) ) ),
inference(cnf_transformation,[],[f1470]) ).
thf(f1470,plain,
! [X0: set_se1612935105at_nat,X1: set_Pr1986765409at_nat] :
( ( ! [X3: set_Pr1986765409at_nat] :
( ( vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK20,X1),X0) = X3 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X3),vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK20,X1),X0)) )
| ( $true != vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X3),X0) ) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK20,X1),X0)),X1) )
& ( $true = vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK20,X1),X0)),X0) ) )
| ( $true != vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X1),X0) )
| ( $true != vAPP(set_se1612935105at_nat,$o,finite1457549322at_nat,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK20])],[f1111,f1469]) ).
thf(f1469,plain,
! [X0: set_se1612935105at_nat,X1: set_Pr1986765409at_nat] :
( ? [X2: set_Pr1986765409at_nat] :
( ! [X3: set_Pr1986765409at_nat] :
( ( X2 = X3 )
| ( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X3),X2) != $true )
| ( $true != vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X3),X0) ) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X2),X1) )
& ( $true = vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X2),X0) ) )
=> ( ! [X3: set_Pr1986765409at_nat] :
( ( vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK20,X1),X0) = X3 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X3),vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK20,X1),X0)) )
| ( $true != vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X3),X0) ) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK20,X1),X0)),X1) )
& ( $true = vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK20,X1),X0)),X0) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1111,plain,
! [X0: set_se1612935105at_nat,X1: set_Pr1986765409at_nat] :
( ? [X2: set_Pr1986765409at_nat] :
( ! [X3: set_Pr1986765409at_nat] :
( ( X2 = X3 )
| ( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X3),X2) != $true )
| ( $true != vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X3),X0) ) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X2),X1) )
& ( $true = vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X2),X0) ) )
| ( $true != vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X1),X0) )
| ( $true != vAPP(set_se1612935105at_nat,$o,finite1457549322at_nat,X0) ) ),
inference(flattening,[],[f1110]) ).
thf(f1110,plain,
! [X0: set_se1612935105at_nat,X1: set_Pr1986765409at_nat] :
( ? [X2: set_Pr1986765409at_nat] :
( ! [X3: set_Pr1986765409at_nat] :
( ( X2 = X3 )
| ( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X3),X2) != $true )
| ( $true != vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X3),X0) ) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X2),X1) )
& ( $true = vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X2),X0) ) )
| ( $true != vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X1),X0) )
| ( $true != vAPP(set_se1612935105at_nat,$o,finite1457549322at_nat,X0) ) ),
inference(ennf_transformation,[],[f557]) ).
thf(f557,plain,
! [X0: set_se1612935105at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_se1612935105at_nat,$o,finite1457549322at_nat,X0) )
=> ( ( $true = vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X1),X0) )
=> ? [X2: set_Pr1986765409at_nat] :
( ! [X3: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X3),X0) )
=> ( ( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X3),X2) = $true )
=> ( X2 = X3 ) ) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X2),X1) )
& ( $true = vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X2),X0) ) ) ) ),
inference(fool_elimination,[],[f556]) ).
thf(f556,plain,
! [X0: set_se1612935105at_nat,X1: set_Pr1986765409at_nat] :
( vAPP(set_se1612935105at_nat,$o,finite1457549322at_nat,X0)
=> ( vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X1),X0)
=> ? [X2: set_Pr1986765409at_nat] :
( ! [X3: set_Pr1986765409at_nat] :
( vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X3),X0)
=> ( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X3),X2)
=> ( X2 = X3 ) ) )
& vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X2),X1)
& vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X2),X0) ) ) ),
inference(rectify,[],[f234]) ).
thf(f234,axiom,
! [X2: set_se1612935105at_nat,X13: set_Pr1986765409at_nat] :
( vAPP(set_se1612935105at_nat,$o,finite1457549322at_nat,X2)
=> ( vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X13),X2)
=> ? [X4: set_Pr1986765409at_nat] :
( ! [X42: set_Pr1986765409at_nat] :
( vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X42),X2)
=> ( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X42),X4)
=> ( X4 = X42 ) ) )
& vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X4),X13)
& vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X4),X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_finite__has__minimal2) ).
thf(f4021,plain,
( spl155_143
| ~ spl155_71
| ~ spl155_89 ),
inference(avatar_split_clause,[],[f3362,f3301,f3223,f4018]) ).
thf(f4018,plain,
( spl155_143
<=> ( edges = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,edges),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_143])]) ).
thf(f3362,plain,
( ( edges = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,edges),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p)) )
| ~ spl155_71
| ~ spl155_89 ),
inference(trivial_inequality_removal,[],[f3357]) ).
thf(f3357,plain,
( ( $true != $true )
| ( edges = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,edges),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p)) )
| ~ spl155_71
| ~ spl155_89 ),
inference(superposition,[],[f3302,f3225]) ).
thf(f4016,plain,
spl155_142,
inference(avatar_split_clause,[],[f2204,f4014]) ).
thf(f2204,plain,
! [X3: set_nat,X0: set_set_nat,X1: set_nat] :
( ( vAPP(set_set_nat,set_nat,vAPP(set_nat,sTfun(set_set_nat,set_nat),sK19,X1),X0) = X3 )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X3),vAPP(set_set_nat,set_nat,vAPP(set_nat,sTfun(set_set_nat,set_nat),sK19,X1),X0)) )
| ( $true != vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X3),X0) )
| ( $true != vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X1),X0) )
| ( $true != vAPP(set_set_nat,$o,finite2012248349et_nat,X0) ) ),
inference(definition_unfolding,[],[f1756,f1650]) ).
thf(f1756,plain,
! [X3: set_nat,X0: set_set_nat,X1: set_nat] :
( ( vAPP(set_set_nat,set_nat,vAPP(set_nat,sTfun(set_set_nat,set_nat),sK19,X1),X0) = X3 )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X3),vAPP(set_set_nat,set_nat,vAPP(set_nat,sTfun(set_set_nat,set_nat),sK19,X1),X0)) )
| ( $true != vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X3),X0) )
| ( $true != vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X1),X0) )
| ( $true != vAPP(set_set_nat,$o,finite2012248349et_nat,X0) ) ),
inference(cnf_transformation,[],[f1468]) ).
thf(f1468,plain,
! [X0: set_set_nat,X1: set_nat] :
( ( ! [X3: set_nat] :
( ( vAPP(set_set_nat,set_nat,vAPP(set_nat,sTfun(set_set_nat,set_nat),sK19,X1),X0) = X3 )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X3),vAPP(set_set_nat,set_nat,vAPP(set_nat,sTfun(set_set_nat,set_nat),sK19,X1),X0)) )
| ( $true != vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X3),X0) ) )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_set_nat,set_nat,vAPP(set_nat,sTfun(set_set_nat,set_nat),sK19,X1),X0)),X1) )
& ( $true = vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,vAPP(set_set_nat,set_nat,vAPP(set_nat,sTfun(set_set_nat,set_nat),sK19,X1),X0)),X0) ) )
| ( $true != vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X1),X0) )
| ( $true != vAPP(set_set_nat,$o,finite2012248349et_nat,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK19])],[f1109,f1467]) ).
thf(f1467,plain,
! [X0: set_set_nat,X1: set_nat] :
( ? [X2: set_nat] :
( ! [X3: set_nat] :
( ( X2 = X3 )
| ( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X3),X2) != $true )
| ( $true != vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X3),X0) ) )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X1) )
& ( $true = vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X2),X0) ) )
=> ( ! [X3: set_nat] :
( ( vAPP(set_set_nat,set_nat,vAPP(set_nat,sTfun(set_set_nat,set_nat),sK19,X1),X0) = X3 )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X3),vAPP(set_set_nat,set_nat,vAPP(set_nat,sTfun(set_set_nat,set_nat),sK19,X1),X0)) )
| ( $true != vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X3),X0) ) )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_set_nat,set_nat,vAPP(set_nat,sTfun(set_set_nat,set_nat),sK19,X1),X0)),X1) )
& ( $true = vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,vAPP(set_set_nat,set_nat,vAPP(set_nat,sTfun(set_set_nat,set_nat),sK19,X1),X0)),X0) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1109,plain,
! [X0: set_set_nat,X1: set_nat] :
( ? [X2: set_nat] :
( ! [X3: set_nat] :
( ( X2 = X3 )
| ( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X3),X2) != $true )
| ( $true != vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X3),X0) ) )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X1) )
& ( $true = vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X2),X0) ) )
| ( $true != vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X1),X0) )
| ( $true != vAPP(set_set_nat,$o,finite2012248349et_nat,X0) ) ),
inference(flattening,[],[f1108]) ).
thf(f1108,plain,
! [X0: set_set_nat,X1: set_nat] :
( ? [X2: set_nat] :
( ! [X3: set_nat] :
( ( X2 = X3 )
| ( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X3),X2) != $true )
| ( $true != vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X3),X0) ) )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X1) )
& ( $true = vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X2),X0) ) )
| ( $true != vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X1),X0) )
| ( $true != vAPP(set_set_nat,$o,finite2012248349et_nat,X0) ) ),
inference(ennf_transformation,[],[f555]) ).
thf(f555,plain,
! [X0: set_set_nat,X1: set_nat] :
( ( $true = vAPP(set_set_nat,$o,finite2012248349et_nat,X0) )
=> ( ( $true = vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X1),X0) )
=> ? [X2: set_nat] :
( ! [X3: set_nat] :
( ( $true = vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X3),X0) )
=> ( ( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X3),X2) = $true )
=> ( X2 = X3 ) ) )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X1) )
& ( $true = vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X2),X0) ) ) ) ),
inference(fool_elimination,[],[f554]) ).
thf(f554,plain,
! [X0: set_set_nat,X1: set_nat] :
( vAPP(set_set_nat,$o,finite2012248349et_nat,X0)
=> ( vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X1),X0)
=> ? [X2: set_nat] :
( ! [X3: set_nat] :
( vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X3),X0)
=> ( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X3),X2)
=> ( X2 = X3 ) ) )
& vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X1)
& vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X2),X0) ) ) ),
inference(rectify,[],[f235]) ).
thf(f235,axiom,
! [X2: set_set_nat,X13: set_nat] :
( vAPP(set_set_nat,$o,finite2012248349et_nat,X2)
=> ( vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X13),X2)
=> ? [X4: set_nat] :
( ! [X42: set_nat] :
( vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X42),X2)
=> ( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X42),X4)
=> ( X4 = X42 ) ) )
& vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X4),X13)
& vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X4),X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_finite__has__minimal2) ).
thf(f4012,plain,
spl155_141,
inference(avatar_split_clause,[],[f2202,f4010]) ).
thf(f2202,plain,
! [X3: set_nat,X0: set_set_nat,X1: set_nat] :
( ( vAPP(set_set_nat,set_nat,vAPP(set_nat,sTfun(set_set_nat,set_nat),sK18,X1),X0) = X3 )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_set_nat,set_nat,vAPP(set_nat,sTfun(set_set_nat,set_nat),sK18,X1),X0)),X3) )
| ( $true != vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X3),X0) )
| ( $true != vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X1),X0) )
| ( $true != vAPP(set_set_nat,$o,finite2012248349et_nat,X0) ) ),
inference(definition_unfolding,[],[f1753,f1650]) ).
thf(f1753,plain,
! [X3: set_nat,X0: set_set_nat,X1: set_nat] :
( ( vAPP(set_set_nat,set_nat,vAPP(set_nat,sTfun(set_set_nat,set_nat),sK18,X1),X0) = X3 )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_set_nat,set_nat,vAPP(set_nat,sTfun(set_set_nat,set_nat),sK18,X1),X0)),X3) )
| ( $true != vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X3),X0) )
| ( $true != vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X1),X0) )
| ( $true != vAPP(set_set_nat,$o,finite2012248349et_nat,X0) ) ),
inference(cnf_transformation,[],[f1466]) ).
thf(f1466,plain,
! [X0: set_set_nat,X1: set_nat] :
( ( ! [X3: set_nat] :
( ( vAPP(set_set_nat,set_nat,vAPP(set_nat,sTfun(set_set_nat,set_nat),sK18,X1),X0) = X3 )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_set_nat,set_nat,vAPP(set_nat,sTfun(set_set_nat,set_nat),sK18,X1),X0)),X3) )
| ( $true != vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X3),X0) ) )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X1),vAPP(set_set_nat,set_nat,vAPP(set_nat,sTfun(set_set_nat,set_nat),sK18,X1),X0)) )
& ( $true = vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,vAPP(set_set_nat,set_nat,vAPP(set_nat,sTfun(set_set_nat,set_nat),sK18,X1),X0)),X0) ) )
| ( $true != vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X1),X0) )
| ( $true != vAPP(set_set_nat,$o,finite2012248349et_nat,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK18])],[f1107,f1465]) ).
thf(f1465,plain,
! [X0: set_set_nat,X1: set_nat] :
( ? [X2: set_nat] :
( ! [X3: set_nat] :
( ( X2 = X3 )
| ( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X3) != $true )
| ( $true != vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X3),X0) ) )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X1),X2) )
& ( $true = vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X2),X0) ) )
=> ( ! [X3: set_nat] :
( ( vAPP(set_set_nat,set_nat,vAPP(set_nat,sTfun(set_set_nat,set_nat),sK18,X1),X0) = X3 )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_set_nat,set_nat,vAPP(set_nat,sTfun(set_set_nat,set_nat),sK18,X1),X0)),X3) )
| ( $true != vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X3),X0) ) )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X1),vAPP(set_set_nat,set_nat,vAPP(set_nat,sTfun(set_set_nat,set_nat),sK18,X1),X0)) )
& ( $true = vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,vAPP(set_set_nat,set_nat,vAPP(set_nat,sTfun(set_set_nat,set_nat),sK18,X1),X0)),X0) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1107,plain,
! [X0: set_set_nat,X1: set_nat] :
( ? [X2: set_nat] :
( ! [X3: set_nat] :
( ( X2 = X3 )
| ( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X3) != $true )
| ( $true != vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X3),X0) ) )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X1),X2) )
& ( $true = vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X2),X0) ) )
| ( $true != vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X1),X0) )
| ( $true != vAPP(set_set_nat,$o,finite2012248349et_nat,X0) ) ),
inference(flattening,[],[f1106]) ).
thf(f1106,plain,
! [X0: set_set_nat,X1: set_nat] :
( ? [X2: set_nat] :
( ! [X3: set_nat] :
( ( X2 = X3 )
| ( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X3) != $true )
| ( $true != vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X3),X0) ) )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X1),X2) )
& ( $true = vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X2),X0) ) )
| ( $true != vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X1),X0) )
| ( $true != vAPP(set_set_nat,$o,finite2012248349et_nat,X0) ) ),
inference(ennf_transformation,[],[f553]) ).
thf(f553,plain,
! [X0: set_set_nat,X1: set_nat] :
( ( $true = vAPP(set_set_nat,$o,finite2012248349et_nat,X0) )
=> ( ( $true = vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X1),X0) )
=> ? [X2: set_nat] :
( ! [X3: set_nat] :
( ( $true = vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X3),X0) )
=> ( ( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X3) = $true )
=> ( X2 = X3 ) ) )
& ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X1),X2) )
& ( $true = vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X2),X0) ) ) ) ),
inference(fool_elimination,[],[f552]) ).
thf(f552,plain,
! [X0: set_set_nat,X1: set_nat] :
( vAPP(set_set_nat,$o,finite2012248349et_nat,X0)
=> ( vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X1),X0)
=> ? [X2: set_nat] :
( ! [X3: set_nat] :
( vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X3),X0)
=> ( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X3)
=> ( X2 = X3 ) ) )
& vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X1),X2)
& vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X2),X0) ) ) ),
inference(rectify,[],[f238]) ).
thf(f238,axiom,
! [X2: set_set_nat,X13: set_nat] :
( vAPP(set_set_nat,$o,finite2012248349et_nat,X2)
=> ( vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X13),X2)
=> ? [X4: set_nat] :
( ! [X42: set_nat] :
( vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X42),X2)
=> ( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X4),X42)
=> ( X4 = X42 ) ) )
& vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X13),X4)
& vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X4),X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_finite__has__maximal2) ).
thf(f3980,plain,
spl155_140,
inference(avatar_split_clause,[],[f2336,f3978]) ).
thf(f3978,plain,
( spl155_140
<=> ! [X4: nat,X0: nat > $o,X2: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X4),vAPP(sTfun(nat,$o),nat,sK60,X0)) )
| ( $true != vAPP(nat,$o,X0,X4) )
| ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK61,X2),X0)) )
| ( $true != vAPP(nat,$o,X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_140])]) ).
thf(f2336,plain,
! [X2: nat,X0: nat > $o,X1: nat,X4: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X4),vAPP(sTfun(nat,$o),nat,sK60,X0)) )
| ( $true != vAPP(nat,$o,X0,X4) )
| ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK61,X2),X0)) )
| ( $true != vAPP(nat,$o,X0,X1) ) ),
inference(definition_unfolding,[],[f1902,f1646]) ).
thf(f1902,plain,
! [X2: nat,X0: nat > $o,X1: nat,X4: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),vAPP(sTfun(nat,$o),nat,sK60,X0)) )
| ( $true != vAPP(nat,$o,X0,X4) )
| ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK61,X2),X0)) )
| ( $true != vAPP(nat,$o,X0,X1) ) ),
inference(cnf_transformation,[],[f1520]) ).
thf(f3970,plain,
spl155_139,
inference(avatar_split_clause,[],[f2272,f3968]) ).
thf(f2272,plain,
! [X0: nat,X1: product_prod_nat_nat > a] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),reachableNodes_a,X1),X0)),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X1)) )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X1)) ) ),
inference(definition_unfolding,[],[f1829,f1650]) ).
thf(f1829,plain,
! [X0: nat,X1: product_prod_nat_nat > a] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),reachableNodes_a,X1),X0)),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X1)) )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X1)) ) ),
inference(cnf_transformation,[],[f1199]) ).
thf(f1199,plain,
! [X0: nat,X1: product_prod_nat_nat > a] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),reachableNodes_a,X1),X0)),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X1)) )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X1)) ) ),
inference(ennf_transformation,[],[f673]) ).
thf(f673,plain,
! [X0: nat,X1: product_prod_nat_nat > a] :
( ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X1)) )
=> ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),reachableNodes_a,X1),X0)),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X1)) ) ),
inference(fool_elimination,[],[f672]) ).
thf(f672,plain,
! [X0: nat,X1: product_prod_nat_nat > a] :
( vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X1))
=> vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),reachableNodes_a,X1),X0)),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X1)) ),
inference(rectify,[],[f169]) ).
thf(f169,axiom,
! [X10: nat,X9: product_prod_nat_nat > a] :
( vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X10),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X9))
=> vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),reachableNodes_a,X9),X10)),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X9)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_Graph_Oreachable__ss__V) ).
thf(f3851,plain,
( spl155_138
| ~ spl155_71
| ~ spl155_88 ),
inference(avatar_split_clause,[],[f3350,f3297,f3223,f3848]) ).
thf(f3350,plain,
( ( edges = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p)),edges) )
| ~ spl155_71
| ~ spl155_88 ),
inference(trivial_inequality_removal,[],[f3345]) ).
thf(f3345,plain,
( ( $true != $true )
| ( edges = vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p)),edges) )
| ~ spl155_71
| ~ spl155_88 ),
inference(superposition,[],[f3298,f3225]) ).
thf(f3846,plain,
spl155_137,
inference(avatar_split_clause,[],[f2189,f3844]) ).
thf(f2189,plain,
! [X0: nat > $o,X1: nat > $o] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(sTfun(nat,$o),set_nat,collect_nat,X0)),vAPP(sTfun(nat,$o),set_nat,collect_nat,X1)) )
| ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(sTfun(nat,$o),sTfun(sTfun(nat,$o),nat),sK13,X1),X0)) ) ),
inference(definition_unfolding,[],[f1735,f1650]) ).
thf(f1735,plain,
! [X0: nat > $o,X1: nat > $o] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(sTfun(nat,$o),set_nat,collect_nat,X0)),vAPP(sTfun(nat,$o),set_nat,collect_nat,X1)) )
| ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(sTfun(nat,$o),sTfun(sTfun(nat,$o),nat),sK13,X1),X0)) ) ),
inference(cnf_transformation,[],[f1452]) ).
thf(f1452,plain,
! [X0: nat > $o,X1: nat > $o] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(sTfun(nat,$o),set_nat,collect_nat,X0)),vAPP(sTfun(nat,$o),set_nat,collect_nat,X1)) )
| ( ( $true != vAPP(nat,$o,X1,vAPP(sTfun(nat,$o),nat,vAPP(sTfun(nat,$o),sTfun(sTfun(nat,$o),nat),sK13,X1),X0)) )
& ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(sTfun(nat,$o),sTfun(sTfun(nat,$o),nat),sK13,X1),X0)) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f1099,f1451]) ).
thf(f1451,plain,
! [X0: nat > $o,X1: nat > $o] :
( ? [X2: nat] :
( ( $true != vAPP(nat,$o,X1,X2) )
& ( $true = vAPP(nat,$o,X0,X2) ) )
=> ( ( $true != vAPP(nat,$o,X1,vAPP(sTfun(nat,$o),nat,vAPP(sTfun(nat,$o),sTfun(sTfun(nat,$o),nat),sK13,X1),X0)) )
& ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(sTfun(nat,$o),sTfun(sTfun(nat,$o),nat),sK13,X1),X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1099,plain,
! [X0: nat > $o,X1: nat > $o] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(sTfun(nat,$o),set_nat,collect_nat,X0)),vAPP(sTfun(nat,$o),set_nat,collect_nat,X1)) )
| ? [X2: nat] :
( ( $true != vAPP(nat,$o,X1,X2) )
& ( $true = vAPP(nat,$o,X0,X2) ) ) ),
inference(ennf_transformation,[],[f543]) ).
thf(f543,plain,
! [X0: nat > $o,X1: nat > $o] :
( ! [X2: nat] :
( ( $true = vAPP(nat,$o,X0,X2) )
=> ( $true = vAPP(nat,$o,X1,X2) ) )
=> ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(sTfun(nat,$o),set_nat,collect_nat,X0)),vAPP(sTfun(nat,$o),set_nat,collect_nat,X1)) ) ),
inference(fool_elimination,[],[f542]) ).
thf(f542,plain,
! [X0: nat > $o,X1: nat > $o] :
( ! [X2: nat] :
( vAPP(nat,$o,X0,X2)
=> vAPP(nat,$o,X1,X2) )
=> vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(sTfun(nat,$o),set_nat,collect_nat,X0)),vAPP(sTfun(nat,$o),set_nat,collect_nat,X1)) ),
inference(rectify,[],[f122]) ).
thf(f122,axiom,
! [X18: nat > $o,X27: nat > $o] :
( ! [X4: nat] :
( vAPP(nat,$o,X18,X4)
=> vAPP(nat,$o,X27,X4) )
=> vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(sTfun(nat,$o),set_nat,collect_nat,X18)),vAPP(sTfun(nat,$o),set_nat,collect_nat,X27)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_Collect__mono) ).
thf(f3842,plain,
spl155_136,
inference(avatar_split_clause,[],[f2188,f3840]) ).
thf(f2188,plain,
! [X0: nat > $o,X1: nat > $o] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(sTfun(nat,$o),set_nat,collect_nat,X0)),vAPP(sTfun(nat,$o),set_nat,collect_nat,X1)) )
| ( $true != vAPP(nat,$o,X1,vAPP(sTfun(nat,$o),nat,vAPP(sTfun(nat,$o),sTfun(sTfun(nat,$o),nat),sK13,X1),X0)) ) ),
inference(definition_unfolding,[],[f1736,f1650]) ).
thf(f1736,plain,
! [X0: nat > $o,X1: nat > $o] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(sTfun(nat,$o),set_nat,collect_nat,X0)),vAPP(sTfun(nat,$o),set_nat,collect_nat,X1)) )
| ( $true != vAPP(nat,$o,X1,vAPP(sTfun(nat,$o),nat,vAPP(sTfun(nat,$o),sTfun(sTfun(nat,$o),nat),sK13,X1),X0)) ) ),
inference(cnf_transformation,[],[f1452]) ).
thf(f3838,plain,
spl155_135,
inference(avatar_split_clause,[],[f2187,f3836]) ).
thf(f2187,plain,
! [X0: product_prod_nat_nat > $o,X1: product_prod_nat_nat > $o] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X0)),vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X1)) )
| ( $true = vAPP(product_prod_nat_nat,$o,X0,vAPP(sTfun(product_prod_nat_nat,$o),product_prod_nat_nat,vAPP(sTfun(product_prod_nat_nat,$o),sTfun(sTfun(product_prod_nat_nat,$o),product_prod_nat_nat),sK12,X1),X0)) ) ),
inference(definition_unfolding,[],[f1733,f1656]) ).
thf(f1733,plain,
! [X0: product_prod_nat_nat > $o,X1: product_prod_nat_nat > $o] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X0)),vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X1)) )
| ( $true = vAPP(product_prod_nat_nat,$o,X0,vAPP(sTfun(product_prod_nat_nat,$o),product_prod_nat_nat,vAPP(sTfun(product_prod_nat_nat,$o),sTfun(sTfun(product_prod_nat_nat,$o),product_prod_nat_nat),sK12,X1),X0)) ) ),
inference(cnf_transformation,[],[f1450]) ).
thf(f1450,plain,
! [X0: product_prod_nat_nat > $o,X1: product_prod_nat_nat > $o] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X0)),vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X1)) )
| ( ( $true != vAPP(product_prod_nat_nat,$o,X1,vAPP(sTfun(product_prod_nat_nat,$o),product_prod_nat_nat,vAPP(sTfun(product_prod_nat_nat,$o),sTfun(sTfun(product_prod_nat_nat,$o),product_prod_nat_nat),sK12,X1),X0)) )
& ( $true = vAPP(product_prod_nat_nat,$o,X0,vAPP(sTfun(product_prod_nat_nat,$o),product_prod_nat_nat,vAPP(sTfun(product_prod_nat_nat,$o),sTfun(sTfun(product_prod_nat_nat,$o),product_prod_nat_nat),sK12,X1),X0)) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f1098,f1449]) ).
thf(f1449,plain,
! [X0: product_prod_nat_nat > $o,X1: product_prod_nat_nat > $o] :
( ? [X2: product_prod_nat_nat] :
( ( $true != vAPP(product_prod_nat_nat,$o,X1,X2) )
& ( $true = vAPP(product_prod_nat_nat,$o,X0,X2) ) )
=> ( ( $true != vAPP(product_prod_nat_nat,$o,X1,vAPP(sTfun(product_prod_nat_nat,$o),product_prod_nat_nat,vAPP(sTfun(product_prod_nat_nat,$o),sTfun(sTfun(product_prod_nat_nat,$o),product_prod_nat_nat),sK12,X1),X0)) )
& ( $true = vAPP(product_prod_nat_nat,$o,X0,vAPP(sTfun(product_prod_nat_nat,$o),product_prod_nat_nat,vAPP(sTfun(product_prod_nat_nat,$o),sTfun(sTfun(product_prod_nat_nat,$o),product_prod_nat_nat),sK12,X1),X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1098,plain,
! [X0: product_prod_nat_nat > $o,X1: product_prod_nat_nat > $o] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X0)),vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X1)) )
| ? [X2: product_prod_nat_nat] :
( ( $true != vAPP(product_prod_nat_nat,$o,X1,X2) )
& ( $true = vAPP(product_prod_nat_nat,$o,X0,X2) ) ) ),
inference(ennf_transformation,[],[f541]) ).
thf(f541,plain,
! [X0: product_prod_nat_nat > $o,X1: product_prod_nat_nat > $o] :
( ! [X2: product_prod_nat_nat] :
( ( $true = vAPP(product_prod_nat_nat,$o,X0,X2) )
=> ( $true = vAPP(product_prod_nat_nat,$o,X1,X2) ) )
=> ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X0)),vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X1)) ) ),
inference(fool_elimination,[],[f540]) ).
thf(f540,plain,
! [X0: product_prod_nat_nat > $o,X1: product_prod_nat_nat > $o] :
( ! [X2: product_prod_nat_nat] :
( vAPP(product_prod_nat_nat,$o,X0,X2)
=> vAPP(product_prod_nat_nat,$o,X1,X2) )
=> vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X0)),vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X1)) ),
inference(rectify,[],[f121]) ).
thf(f121,axiom,
! [X18: product_prod_nat_nat > $o,X27: product_prod_nat_nat > $o] :
( ! [X4: product_prod_nat_nat] :
( vAPP(product_prod_nat_nat,$o,X18,X4)
=> vAPP(product_prod_nat_nat,$o,X27,X4) )
=> vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X18)),vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X27)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_Collect__mono) ).
thf(f3834,plain,
spl155_134,
inference(avatar_split_clause,[],[f2186,f3832]) ).
thf(f3832,plain,
( spl155_134
<=> ! [X0: product_prod_nat_nat > $o,X1: product_prod_nat_nat > $o] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X0)),vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X1)) )
| ( $true != vAPP(product_prod_nat_nat,$o,X1,vAPP(sTfun(product_prod_nat_nat,$o),product_prod_nat_nat,vAPP(sTfun(product_prod_nat_nat,$o),sTfun(sTfun(product_prod_nat_nat,$o),product_prod_nat_nat),sK12,X1),X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_134])]) ).
thf(f2186,plain,
! [X0: product_prod_nat_nat > $o,X1: product_prod_nat_nat > $o] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X0)),vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X1)) )
| ( $true != vAPP(product_prod_nat_nat,$o,X1,vAPP(sTfun(product_prod_nat_nat,$o),product_prod_nat_nat,vAPP(sTfun(product_prod_nat_nat,$o),sTfun(sTfun(product_prod_nat_nat,$o),product_prod_nat_nat),sK12,X1),X0)) ) ),
inference(definition_unfolding,[],[f1734,f1656]) ).
thf(f1734,plain,
! [X0: product_prod_nat_nat > $o,X1: product_prod_nat_nat > $o] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X0)),vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,X1)) )
| ( $true != vAPP(product_prod_nat_nat,$o,X1,vAPP(sTfun(product_prod_nat_nat,$o),product_prod_nat_nat,vAPP(sTfun(product_prod_nat_nat,$o),sTfun(sTfun(product_prod_nat_nat,$o),product_prod_nat_nat),sK12,X1),X0)) ) ),
inference(cnf_transformation,[],[f1450]) ).
thf(f3817,plain,
spl155_133,
inference(avatar_split_clause,[],[f2487,f3814]) ).
thf(f2487,plain,
$true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,c),s),t))),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,c))),
inference(definition_unfolding,[],[f2097,f1646]) ).
thf(f2097,plain,
vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,c),s),t))),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,c))) = $true,
inference(cnf_transformation,[],[f1035]) ).
thf(f1035,plain,
vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,c),s),t))),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,c))) = $true,
inference(fool_elimination,[],[f1034]) ).
thf(f1034,plain,
vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,c),s),t))),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,c))),
inference(rectify,[],[f141]) ).
thf(f141,axiom,
vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,c),s),t))),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,c))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_card__spEdges__le) ).
thf(f3812,plain,
spl155_132,
inference(avatar_split_clause,[],[f2337,f3810]) ).
thf(f2337,plain,
! [X2: nat,X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK60,X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK61,X2),X0)),X2) )
| ( $true != vAPP(nat,$o,X0,X1) ) ),
inference(definition_unfolding,[],[f1901,f1646]) ).
thf(f1901,plain,
! [X2: nat,X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK60,X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK61,X2),X0)),X2) )
| ( $true != vAPP(nat,$o,X0,X1) ) ),
inference(cnf_transformation,[],[f1520]) ).
thf(f3798,plain,
spl155_131,
inference(avatar_split_clause,[],[f2209,f3796]) ).
thf(f3796,plain,
( spl155_131
<=> ! [X0: set_se1612935105at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X1),vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK21,X1),X0)) )
| ( $true != vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X1),X0) )
| ( $true != vAPP(set_se1612935105at_nat,$o,finite1457549322at_nat,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_131])]) ).
thf(f2209,plain,
! [X0: set_se1612935105at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X1),vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK21,X1),X0)) )
| ( $true != vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X1),X0) )
| ( $true != vAPP(set_se1612935105at_nat,$o,finite1457549322at_nat,X0) ) ),
inference(definition_unfolding,[],[f1761,f1656]) ).
thf(f1761,plain,
! [X0: set_se1612935105at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X1),vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK21,X1),X0)) )
| ( $true != vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X1),X0) )
| ( $true != vAPP(set_se1612935105at_nat,$o,finite1457549322at_nat,X0) ) ),
inference(cnf_transformation,[],[f1472]) ).
thf(f3794,plain,
spl155_130,
inference(avatar_split_clause,[],[f2207,f3792]) ).
thf(f3792,plain,
( spl155_130
<=> ! [X0: set_se1612935105at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK20,X1),X0)),X1) )
| ( $true != vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X1),X0) )
| ( $true != vAPP(set_se1612935105at_nat,$o,finite1457549322at_nat,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_130])]) ).
thf(f2207,plain,
! [X0: set_se1612935105at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK20,X1),X0)),X1) )
| ( $true != vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X1),X0) )
| ( $true != vAPP(set_se1612935105at_nat,$o,finite1457549322at_nat,X0) ) ),
inference(definition_unfolding,[],[f1758,f1656]) ).
thf(f1758,plain,
! [X0: set_se1612935105at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK20,X1),X0)),X1) )
| ( $true != vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X1),X0) )
| ( $true != vAPP(set_se1612935105at_nat,$o,finite1457549322at_nat,X0) ) ),
inference(cnf_transformation,[],[f1470]) ).
thf(f3790,plain,
spl155_129,
inference(avatar_split_clause,[],[f2205,f3788]) ).
thf(f3788,plain,
( spl155_129
<=> ! [X0: set_set_nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_set_nat,set_nat,vAPP(set_nat,sTfun(set_set_nat,set_nat),sK19,X1),X0)),X1) )
| ( $true != vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X1),X0) )
| ( $true != vAPP(set_set_nat,$o,finite2012248349et_nat,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_129])]) ).
thf(f2205,plain,
! [X0: set_set_nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_set_nat,set_nat,vAPP(set_nat,sTfun(set_set_nat,set_nat),sK19,X1),X0)),X1) )
| ( $true != vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X1),X0) )
| ( $true != vAPP(set_set_nat,$o,finite2012248349et_nat,X0) ) ),
inference(definition_unfolding,[],[f1755,f1650]) ).
thf(f1755,plain,
! [X0: set_set_nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_set_nat,set_nat,vAPP(set_nat,sTfun(set_set_nat,set_nat),sK19,X1),X0)),X1) )
| ( $true != vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X1),X0) )
| ( $true != vAPP(set_set_nat,$o,finite2012248349et_nat,X0) ) ),
inference(cnf_transformation,[],[f1468]) ).
thf(f3786,plain,
spl155_128,
inference(avatar_split_clause,[],[f2203,f3784]) ).
thf(f3784,plain,
( spl155_128
<=> ! [X0: set_set_nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X1),vAPP(set_set_nat,set_nat,vAPP(set_nat,sTfun(set_set_nat,set_nat),sK18,X1),X0)) )
| ( $true != vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X1),X0) )
| ( $true != vAPP(set_set_nat,$o,finite2012248349et_nat,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_128])]) ).
thf(f2203,plain,
! [X0: set_set_nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X1),vAPP(set_set_nat,set_nat,vAPP(set_nat,sTfun(set_set_nat,set_nat),sK18,X1),X0)) )
| ( $true != vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X1),X0) )
| ( $true != vAPP(set_set_nat,$o,finite2012248349et_nat,X0) ) ),
inference(definition_unfolding,[],[f1752,f1650]) ).
thf(f1752,plain,
! [X0: set_set_nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X1),vAPP(set_set_nat,set_nat,vAPP(set_nat,sTfun(set_set_nat,set_nat),sK18,X1),X0)) )
| ( $true != vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X1),X0) )
| ( $true != vAPP(set_set_nat,$o,finite2012248349et_nat,X0) ) ),
inference(cnf_transformation,[],[f1466]) ).
thf(f3774,plain,
spl155_127,
inference(avatar_split_clause,[],[f2199,f3772]) ).
thf(f2199,plain,
! [X0: nat,X1: set_Pr1986765409at_nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK17,X1),X0))),X0) )
| ( $true != vAPP(nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(nat,$o),sP1,X1),X0) ) ),
inference(definition_unfolding,[],[f1748,f1646]) ).
thf(f1748,plain,
! [X0: nat,X1: set_Pr1986765409at_nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK17,X1),X0))),X0) )
| ( $true != vAPP(nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(nat,$o),sP1,X1),X0) ) ),
inference(cnf_transformation,[],[f1464]) ).
thf(f1464,plain,
! [X0: nat,X1: set_Pr1986765409at_nat] :
( ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK17,X1),X0))),X0) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK17,X1),X0)) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK17,X1),X0)),X1) ) )
| ( $true != vAPP(nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(nat,$o),sP1,X1),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK17])],[f1462,f1463]) ).
thf(f1463,plain,
! [X0: nat,X1: set_Pr1986765409at_nat] :
( ? [X2: set_Pr1986765409at_nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X2)),X0) )
& ( vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X2) = $true )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X2),X1) ) )
=> ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK17,X1),X0))),X0) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK17,X1),X0)) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK17,X1),X0)),X1) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1462,plain,
! [X0: nat,X1: set_Pr1986765409at_nat] :
( ? [X2: set_Pr1986765409at_nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X2)),X0) )
& ( vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X2) = $true )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X2),X1) ) )
| ( $true != vAPP(nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(nat,$o),sP1,X1),X0) ) ),
inference(rectify,[],[f1461]) ).
thf(f1461,plain,
! [X1: nat,X0: set_Pr1986765409at_nat] :
( ? [X2: set_Pr1986765409at_nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X2)),X1) )
& ( vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X2) = $true )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X2),X0) ) )
| ( $true != vAPP(nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(nat,$o),sP1,X0),X1) ) ),
inference(nnf_transformation,[],[f1430]) ).
thf(f1430,plain,
! [X1: nat,X0: set_Pr1986765409at_nat] :
( ? [X2: set_Pr1986765409at_nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X2)),X1) )
& ( vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X2) = $true )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X2),X0) ) )
| ( $true != vAPP(nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(nat,$o),sP1,X0),X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f3770,plain,
spl155_126,
inference(avatar_split_clause,[],[f2190,f3768]) ).
thf(f2190,plain,
! [X0: nat,X1: set_nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_nat,nat,finite_card_nat,vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK14,X1),X0))),X0) )
| ( $true != vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,X1),X0) ) ),
inference(definition_unfolding,[],[f1739,f1646]) ).
thf(f1739,plain,
! [X0: nat,X1: set_nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,finite_card_nat,vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK14,X1),X0))),X0) )
| ( $true != vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,X1),X0) ) ),
inference(cnf_transformation,[],[f1456]) ).
thf(f3766,plain,
( spl155_125
| spl155_31
| ~ spl155_119 ),
inference(avatar_split_clause,[],[f3692,f3632,f2966,f3763]) ).
thf(f3692,plain,
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),edges) )
| spl155_31
| ~ spl155_119 ),
inference(trivial_inequality_removal,[],[f3670]) ).
thf(f3670,plain,
( ( $true != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),edges)),edges) )
| spl155_31
| ~ spl155_119 ),
inference(superposition,[],[f2968,f3633]) ).
thf(f3713,plain,
spl155_124,
inference(avatar_split_clause,[],[f2529,f3711]) ).
thf(f2529,plain,
! [X2: nat,X0: nat,X1: list_P559422087at_nat] :
( ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),vAPP($o,sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat))),sK85,vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2)),X2),X1),X0)),vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),vAPP($o,sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat))),sK86,vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2)),X2),X1),X0))),vAPP(nat,list_P559422087at_nat,vAPP(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat)),vAPP($o,sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat))),sK87,vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2)),X2),X1),X0)) = X1 )
| ( nil_Pr1308055047at_nat = X1 ) ),
inference(equality_resolution,[],[f2004]) ).
thf(f2004,plain,
! [X2: nat,X3: $o,X0: nat,X1: list_P559422087at_nat] :
( ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),vAPP($o,sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat))),sK85,X3),X2),X1),X0)),vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),vAPP($o,sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat))),sK86,X3),X2),X1),X0))),vAPP(nat,list_P559422087at_nat,vAPP(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat)),vAPP($o,sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat))),sK87,X3),X2),X1),X0)) = X1 )
| ( nil_Pr1308055047at_nat = X1 )
| ( vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2) != X3 ) ),
inference(cnf_transformation,[],[f1548]) ).
thf(f3709,plain,
spl155_123,
inference(avatar_split_clause,[],[f2486,f3706]) ).
thf(f2486,plain,
$true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,c),s),t)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),
inference(definition_unfolding,[],[f2096,f1656]) ).
thf(f2096,plain,
vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,c),s),t)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) = $true,
inference(cnf_transformation,[],[f1033]) ).
thf(f1033,plain,
vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,c),s),t)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) = $true,
inference(fool_elimination,[],[f1032]) ).
thf(f1032,plain,
vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,c),s),t)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),
inference(rectify,[],[f18]) ).
thf(f18,axiom,
vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,c),s),t)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_spEdges__ss__E) ).
thf(f3704,plain,
spl155_122,
inference(avatar_split_clause,[],[f2368,f3702]) ).
thf(f2368,plain,
! [X2: product_prod_nat_nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X2),X1) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X2),X0) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X1) ) ),
inference(definition_unfolding,[],[f1936,f1656]) ).
thf(f1936,plain,
! [X2: product_prod_nat_nat,X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X2),X1) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X2),X0) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1274]) ).
thf(f1274,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat,X2: product_prod_nat_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X2),X1) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X2),X0) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1) ) ),
inference(flattening,[],[f1273]) ).
thf(f1273,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat,X2: product_prod_nat_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X2),X1) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X2),X0) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1) ) ),
inference(ennf_transformation,[],[f835]) ).
thf(f835,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat,X2: product_prod_nat_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1) )
=> ( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X2),X0) )
=> ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X2),X1) ) ) ),
inference(fool_elimination,[],[f834]) ).
thf(f834,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat,X2: product_prod_nat_nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1)
=> ( vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X2),X0)
=> vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X2),X1) ) ),
inference(rectify,[],[f135]) ).
thf(f135,axiom,
! [X2: set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat,X9: product_prod_nat_nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X2),X3)
=> ( vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X9),X2)
=> vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X9),X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_subsetD) ).
thf(f3700,plain,
spl155_121,
inference(avatar_split_clause,[],[f2350,f3698]) ).
thf(f2350,plain,
! [X2: nat,X0: set_nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X2),X1) )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X2),X0) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),X1) ) ),
inference(definition_unfolding,[],[f1916,f1650]) ).
thf(f1916,plain,
! [X2: nat,X0: set_nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X2),X1) )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X2),X0) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1242]) ).
thf(f1242,plain,
! [X0: set_nat,X1: set_nat,X2: nat] :
( ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X2),X1) )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X2),X0) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1) ) ),
inference(flattening,[],[f1241]) ).
thf(f1241,plain,
! [X0: set_nat,X1: set_nat,X2: nat] :
( ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X2),X1) )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X2),X0) )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1) ) ),
inference(ennf_transformation,[],[f795]) ).
thf(f795,plain,
! [X0: set_nat,X1: set_nat,X2: nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1) )
=> ( ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X2),X0) )
=> ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X2),X1) ) ) ),
inference(fool_elimination,[],[f794]) ).
thf(f794,plain,
! [X0: set_nat,X1: set_nat,X2: nat] :
( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1)
=> ( vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X2),X0)
=> vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X2),X1) ) ),
inference(rectify,[],[f138]) ).
thf(f138,axiom,
! [X2: set_nat,X3: set_nat,X5: nat] :
( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X3)
=> ( vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X5),X2)
=> vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X5),X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_in__mono) ).
thf(f3638,plain,
spl155_120,
inference(avatar_split_clause,[],[f2200,f3636]) ).
thf(f2200,plain,
! [X0: nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK17,X1),X0)),X1) )
| ( $true != vAPP(nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(nat,$o),sP1,X1),X0) ) ),
inference(definition_unfolding,[],[f1746,f1656]) ).
thf(f1746,plain,
! [X0: nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK17,X1),X0)),X1) )
| ( $true != vAPP(nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(nat,$o),sP1,X1),X0) ) ),
inference(cnf_transformation,[],[f1464]) ).
thf(f3634,plain,
spl155_119,
inference(avatar_split_clause,[],[f2198,f3632]) ).
thf(f2198,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X1) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,X1),X0)),X0) ) ),
inference(definition_unfolding,[],[f1744,f1656]) ).
thf(f1744,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,X1),X0)),X0) ) ),
inference(cnf_transformation,[],[f1460]) ).
thf(f1460,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1) )
| ( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,X1),X0)),X1) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,X1),X0)),X0) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK16])],[f1103,f1459]) ).
thf(f1459,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ? [X2: product_prod_nat_nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X2),X1) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X2),X0) ) )
=> ( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,X1),X0)),X1) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,X1),X0)),X0) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1103,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1) )
| ? [X2: product_prod_nat_nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X2),X1) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X2),X0) ) ) ),
inference(ennf_transformation,[],[f549]) ).
thf(f549,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ! [X2: product_prod_nat_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X2),X0) )
=> ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X2),X1) ) )
=> ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1) ) ),
inference(fool_elimination,[],[f548]) ).
thf(f548,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ! [X2: product_prod_nat_nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X2),X0)
=> vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X2),X1) )
=> vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1) ),
inference(rectify,[],[f10]) ).
thf(f10,axiom,
! [X2: set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat] :
( ! [X4: product_prod_nat_nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X4),X2)
=> vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X4),X3) )
=> vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X2),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_subsetI) ).
thf(f3630,plain,
spl155_118,
inference(avatar_split_clause,[],[f2197,f3628]) ).
thf(f2197,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X1) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,X1),X0)),X1) ) ),
inference(definition_unfolding,[],[f1745,f1656]) ).
thf(f1745,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(set_Pr1986765409at_nat,product_prod_nat_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,product_prod_nat_nat),sK16,X1),X0)),X1) ) ),
inference(cnf_transformation,[],[f1460]) ).
thf(f3626,plain,
spl155_117,
inference(avatar_split_clause,[],[f2196,f3624]) ).
thf(f2196,plain,
! [X0: set_nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),X1) )
| ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,vAPP(set_nat,nat,vAPP(set_nat,sTfun(set_nat,nat),sK15,X1),X0)),X0) ) ),
inference(definition_unfolding,[],[f1742,f1650]) ).
thf(f1742,plain,
! [X0: set_nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1) )
| ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,vAPP(set_nat,nat,vAPP(set_nat,sTfun(set_nat,nat),sK15,X1),X0)),X0) ) ),
inference(cnf_transformation,[],[f1458]) ).
thf(f1458,plain,
! [X0: set_nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1) )
| ( ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,vAPP(set_nat,nat,vAPP(set_nat,sTfun(set_nat,nat),sK15,X1),X0)),X1) )
& ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,vAPP(set_nat,nat,vAPP(set_nat,sTfun(set_nat,nat),sK15,X1),X0)),X0) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15])],[f1102,f1457]) ).
thf(f1457,plain,
! [X0: set_nat,X1: set_nat] :
( ? [X2: nat] :
( ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X2),X1) )
& ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X2),X0) ) )
=> ( ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,vAPP(set_nat,nat,vAPP(set_nat,sTfun(set_nat,nat),sK15,X1),X0)),X1) )
& ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,vAPP(set_nat,nat,vAPP(set_nat,sTfun(set_nat,nat),sK15,X1),X0)),X0) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1102,plain,
! [X0: set_nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1) )
| ? [X2: nat] :
( ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X2),X1) )
& ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X2),X0) ) ) ),
inference(ennf_transformation,[],[f547]) ).
thf(f547,plain,
! [X0: set_nat,X1: set_nat] :
( ! [X2: nat] :
( ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X2),X0) )
=> ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X2),X1) ) )
=> ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1) ) ),
inference(fool_elimination,[],[f546]) ).
thf(f546,plain,
! [X0: set_nat,X1: set_nat] :
( ! [X2: nat] :
( vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X2),X0)
=> vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X2),X1) )
=> vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1) ),
inference(rectify,[],[f11]) ).
thf(f11,axiom,
! [X2: set_nat,X3: set_nat] :
( ! [X4: nat] :
( vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X4),X2)
=> vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X4),X3) )
=> vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_subsetI) ).
thf(f3622,plain,
spl155_116,
inference(avatar_split_clause,[],[f2195,f3620]) ).
thf(f2195,plain,
! [X0: set_nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),X1) )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,vAPP(set_nat,nat,vAPP(set_nat,sTfun(set_nat,nat),sK15,X1),X0)),X1) ) ),
inference(definition_unfolding,[],[f1743,f1650]) ).
thf(f1743,plain,
! [X0: set_nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1) )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,vAPP(set_nat,nat,vAPP(set_nat,sTfun(set_nat,nat),sK15,X1),X0)),X1) ) ),
inference(cnf_transformation,[],[f1458]) ).
thf(f3618,plain,
spl155_115,
inference(avatar_split_clause,[],[f2192,f3616]) ).
thf(f2192,plain,
! [X0: nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK14,X1),X0)),X1) )
| ( $true != vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,X1),X0) ) ),
inference(definition_unfolding,[],[f1737,f1650]) ).
thf(f1737,plain,
! [X0: nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK14,X1),X0)),X1) )
| ( $true != vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,X1),X0) ) ),
inference(cnf_transformation,[],[f1456]) ).
thf(f3526,plain,
spl155_114,
inference(avatar_split_clause,[],[f2319,f3524]) ).
thf(f2319,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X2),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP2,X2),X1),X0) ) ),
inference(definition_unfolding,[],[f1877,f1646]) ).
thf(f1877,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP2,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f1495]) ).
thf(f1495,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X1) ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP2,X2),X1),X0) ) ),
inference(rectify,[],[f1494]) ).
thf(f1494,plain,
! [X2: nat,X1: nat,X0: nat] :
( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP2,X0),X1),X2) ) ),
inference(nnf_transformation,[],[f1432]) ).
thf(f3522,plain,
spl155_113,
inference(avatar_split_clause,[],[f2318,f3520]) ).
thf(f2318,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X1),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP2,X2),X1),X0) ) ),
inference(definition_unfolding,[],[f1878,f1646]) ).
thf(f1878,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP2,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f1495]) ).
thf(f3518,plain,
spl155_112,
inference(avatar_split_clause,[],[f2317,f3516]) ).
thf(f2317,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X2),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP3,X2),X1),X0) ) ),
inference(definition_unfolding,[],[f1875,f1646]) ).
thf(f1875,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP3,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f1493]) ).
thf(f1493,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X1) ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP3,X2),X1),X0) ) ),
inference(rectify,[],[f1492]) ).
thf(f1492,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP3,X1),X0),X2) ) ),
inference(nnf_transformation,[],[f1433]) ).
thf(f3514,plain,
spl155_111,
inference(avatar_split_clause,[],[f2316,f3512]) ).
thf(f2316,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X1),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP3,X2),X1),X0) ) ),
inference(definition_unfolding,[],[f1876,f1646]) ).
thf(f1876,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP3,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f1493]) ).
thf(f3510,plain,
spl155_110,
inference(avatar_split_clause,[],[f2315,f3508]) ).
thf(f2315,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X2),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP4,X2),X1),X0) ) ),
inference(definition_unfolding,[],[f1873,f1646]) ).
thf(f1873,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP4,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f1491]) ).
thf(f1491,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X1) ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP4,X2),X1),X0) ) ),
inference(rectify,[],[f1490]) ).
thf(f1490,plain,
! [X1: nat,X2: nat,X0: nat] :
( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X1) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP4,X0),X2),X1) ) ),
inference(nnf_transformation,[],[f1434]) ).
thf(f3506,plain,
spl155_109,
inference(avatar_split_clause,[],[f2314,f3504]) ).
thf(f2314,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X1),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP4,X2),X1),X0) ) ),
inference(definition_unfolding,[],[f1874,f1646]) ).
thf(f1874,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP4,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f1491]) ).
thf(f3502,plain,
spl155_108,
inference(avatar_split_clause,[],[f2313,f3500]) ).
thf(f2313,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X2),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP5,X2),X1),X0) ) ),
inference(definition_unfolding,[],[f1871,f1646]) ).
thf(f1871,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP5,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f1489]) ).
thf(f1489,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X1) ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP5,X2),X1),X0) ) ),
inference(nnf_transformation,[],[f1435]) ).
thf(f3498,plain,
spl155_107,
inference(avatar_split_clause,[],[f2312,f3496]) ).
thf(f2312,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X1),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP5,X2),X1),X0) ) ),
inference(definition_unfolding,[],[f1872,f1646]) ).
thf(f1872,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP5,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f1489]) ).
thf(f3494,plain,
( spl155_106
| ~ spl155_69
| ~ spl155_88 ),
inference(avatar_split_clause,[],[f3353,f3297,f3213,f3492]) ).
thf(f3213,plain,
( spl155_69
<=> ! [X0: set_Pr1986765409at_nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_69])]) ).
thf(f3353,plain,
( ! [X0: set_Pr1986765409at_nat] : ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X0) = X0 )
| ~ spl155_69
| ~ spl155_88 ),
inference(trivial_inequality_removal,[],[f3342]) ).
thf(f3342,plain,
( ! [X0: set_Pr1986765409at_nat] :
( ( $true != $true )
| ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X0) = X0 ) )
| ~ spl155_69
| ~ spl155_88 ),
inference(superposition,[],[f3298,f3214]) ).
thf(f3214,plain,
( ! [X0: set_Pr1986765409at_nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X0) )
| ~ spl155_69 ),
inference(avatar_component_clause,[],[f3213]) ).
thf(f3490,plain,
spl155_105,
inference(avatar_split_clause,[],[f2270,f3488]) ).
thf(f2270,plain,
! [X0: nat,X1: set_Pr1986765409at_nat] :
( ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK28,X1),X0)) = X0 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)) ) ),
inference(definition_unfolding,[],[f1825,f1646]) ).
thf(f1825,plain,
! [X0: nat,X1: set_Pr1986765409at_nat] :
( ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK28,X1),X0)) = X0 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)) ) ),
inference(cnf_transformation,[],[f1484]) ).
thf(f3486,plain,
spl155_104,
inference(avatar_split_clause,[],[f2269,f3484]) ).
thf(f2269,plain,
! [X0: nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK28,X1),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)) ) ),
inference(definition_unfolding,[],[f1826,f1646]) ).
thf(f1826,plain,
! [X0: nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK28,X1),X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1)) ) ),
inference(cnf_transformation,[],[f1484]) ).
thf(f3482,plain,
spl155_103,
inference(avatar_split_clause,[],[f2267,f3480]) ).
thf(f2267,plain,
! [X0: nat,X1: set_nat] :
( ( vAPP(set_nat,nat,finite_card_nat,vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK27,X1),X0)) = X0 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),vAPP(set_nat,nat,finite_card_nat,X1)) ) ),
inference(definition_unfolding,[],[f1822,f1646]) ).
thf(f1822,plain,
! [X0: nat,X1: set_nat] :
( ( vAPP(set_nat,nat,finite_card_nat,vAPP(nat,set_nat,vAPP(set_nat,sTfun(nat,set_nat),sK27,X1),X0)) = X0 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(set_nat,nat,finite_card_nat,X1)) ) ),
inference(cnf_transformation,[],[f1482]) ).
thf(f3478,plain,
spl155_102,
inference(avatar_split_clause,[],[f2220,f3476]) ).
thf(f2220,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( X0 = X1 )
| ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0) != vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X1),X0) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) ) ),
inference(definition_unfolding,[],[f1773,f1656]) ).
thf(f1773,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( X0 = X1 )
| ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0) != vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X1),X0) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) ) ),
inference(cnf_transformation,[],[f1127]) ).
thf(f1127,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( X0 = X1 )
| ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0) != vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X1),X0) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) ) ),
inference(flattening,[],[f1126]) ).
thf(f1126,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( X0 = X1 )
| ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0) != vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X1),X0) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) ) ),
inference(ennf_transformation,[],[f573]) ).
thf(f573,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) )
=> ( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X1),X0) )
=> ( ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0) = vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1) )
=> ( X0 = X1 ) ) ) ),
inference(fool_elimination,[],[f572]) ).
thf(f572,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0)
=> ( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X1),X0)
=> ( ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0) = vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X1) )
=> ( X0 = X1 ) ) ) ),
inference(rectify,[],[f333]) ).
thf(f333,axiom,
! [X3: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat] :
( vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X3)
=> ( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X2),X3)
=> ( ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X2) = vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X3) )
=> ( X2 = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_332_card__subset__eq) ).
thf(f3442,plain,
( spl155_101
| ~ spl155_68
| ~ spl155_86 ),
inference(avatar_split_clause,[],[f3333,f3289,f3209,f3440]) ).
thf(f3440,plain,
( spl155_101
<=> ! [X0: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_101])]) ).
thf(f3333,plain,
( ! [X0: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X0) = X0 )
| ~ spl155_68
| ~ spl155_86 ),
inference(trivial_inequality_removal,[],[f3326]) ).
thf(f3326,plain,
( ! [X0: nat] :
( ( $true != $true )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X0) = X0 ) )
| ~ spl155_68
| ~ spl155_86 ),
inference(superposition,[],[f3290,f3210]) ).
thf(f3438,plain,
spl155_100,
inference(avatar_split_clause,[],[f2507,f3436]) ).
thf(f2507,plain,
! [X2: product_prod_nat_nat,X1: list_P559422087at_nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(list_P559422087at_nat,nat,size_s1990949619at_nat,vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,X2),X1))),vAPP(list_P559422087at_nat,nat,size_s1990949619at_nat,X1)) ),
inference(equality_resolution,[],[f2383]) ).
thf(f2383,plain,
! [X2: product_prod_nat_nat,X0: list_P559422087at_nat,X1: list_P559422087at_nat] :
( ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,X2),X1) != X0 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(list_P559422087at_nat,nat,size_s1990949619at_nat,X0)),vAPP(list_P559422087at_nat,nat,size_s1990949619at_nat,X1)) ) ),
inference(definition_unfolding,[],[f1951,f1646]) ).
thf(f1951,plain,
! [X2: product_prod_nat_nat,X0: list_P559422087at_nat,X1: list_P559422087at_nat] :
( ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,X2),X1) != X0 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(list_P559422087at_nat,nat,size_s1990949619at_nat,X0)),vAPP(list_P559422087at_nat,nat,size_s1990949619at_nat,X1)) ) ),
inference(cnf_transformation,[],[f1299]) ).
thf(f1299,plain,
! [X0: list_P559422087at_nat,X1: list_P559422087at_nat,X2: product_prod_nat_nat] :
( ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,X2),X1) != X0 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(list_P559422087at_nat,nat,size_s1990949619at_nat,X0)),vAPP(list_P559422087at_nat,nat,size_s1990949619at_nat,X1)) ) ),
inference(ennf_transformation,[],[f865]) ).
thf(f865,plain,
! [X0: list_P559422087at_nat,X1: list_P559422087at_nat,X2: product_prod_nat_nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(list_P559422087at_nat,nat,size_s1990949619at_nat,X0)),vAPP(list_P559422087at_nat,nat,size_s1990949619at_nat,X1)) )
=> ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,X2),X1) != X0 ) ),
inference(fool_elimination,[],[f864]) ).
thf(f864,plain,
! [X0: list_P559422087at_nat,X1: list_P559422087at_nat,X2: product_prod_nat_nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(list_P559422087at_nat,nat,size_s1990949619at_nat,X0)),vAPP(list_P559422087at_nat,nat,size_s1990949619at_nat,X1))
=> ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,X2),X1) != X0 ) ),
inference(rectify,[],[f343]) ).
thf(f343,axiom,
! [X40: list_P559422087at_nat,X57: list_P559422087at_nat,X5: product_prod_nat_nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(list_P559422087at_nat,nat,size_s1990949619at_nat,X40)),vAPP(list_P559422087at_nat,nat,size_s1990949619at_nat,X57))
=> ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,X5),X57) != X40 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_342_impossible__Cons) ).
thf(f3434,plain,
spl155_99,
inference(avatar_split_clause,[],[f2299,f3432]) ).
thf(f2299,plain,
! [X0: product_prod_nat_nat > a,X1: nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),outgoing_a,X0),X1)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) ),
inference(definition_unfolding,[],[f1856,f1656]) ).
thf(f1856,plain,
! [X0: product_prod_nat_nat > a,X1: nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),outgoing_a,X0),X1)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) ),
inference(cnf_transformation,[],[f727]) ).
thf(f727,plain,
! [X0: product_prod_nat_nat > a,X1: nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),outgoing_a,X0),X1)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) ),
inference(fool_elimination,[],[f726]) ).
thf(f726,plain,
! [X0: product_prod_nat_nat > a,X1: nat] : vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),outgoing_a,X0),X1)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)),
inference(rectify,[],[f146]) ).
thf(f146,axiom,
! [X9: product_prod_nat_nat > a,X1: nat] : vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),outgoing_a,X9),X1)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X9)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_Graph_Ooutgoing__edges) ).
thf(f3430,plain,
spl155_98,
inference(avatar_split_clause,[],[f2298,f3428]) ).
thf(f2298,plain,
! [X0: product_prod_nat_nat > a,X1: nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),incoming_a,X0),X1)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) ),
inference(definition_unfolding,[],[f1855,f1656]) ).
thf(f1855,plain,
! [X0: product_prod_nat_nat > a,X1: nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),incoming_a,X0),X1)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) ),
inference(cnf_transformation,[],[f725]) ).
thf(f725,plain,
! [X0: product_prod_nat_nat > a,X1: nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),incoming_a,X0),X1)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) ),
inference(fool_elimination,[],[f724]) ).
thf(f724,plain,
! [X0: product_prod_nat_nat > a,X1: nat] : vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),incoming_a,X0),X1)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)),
inference(rectify,[],[f145]) ).
thf(f145,axiom,
! [X9: product_prod_nat_nat > a,X1: nat] : vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_Pr1986765409at_nat),incoming_a,X9),X1)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X9)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_Graph_Oincoming__edges) ).
thf(f3426,plain,
spl155_97,
inference(avatar_split_clause,[],[f2297,f3424]) ).
thf(f2297,plain,
! [X0: product_prod_nat_nat > a,X1: set_nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),outgoing_a2,X0),X1)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) ),
inference(definition_unfolding,[],[f1854,f1656]) ).
thf(f1854,plain,
! [X0: product_prod_nat_nat > a,X1: set_nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),outgoing_a2,X0),X1)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) ),
inference(cnf_transformation,[],[f723]) ).
thf(f723,plain,
! [X0: product_prod_nat_nat > a,X1: set_nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),outgoing_a2,X0),X1)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) ),
inference(fool_elimination,[],[f722]) ).
thf(f722,plain,
! [X0: product_prod_nat_nat > a,X1: set_nat] : vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),outgoing_a2,X0),X1)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)),
inference(rectify,[],[f144]) ).
thf(f144,axiom,
! [X9: product_prod_nat_nat > a,X0: set_nat] : vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),outgoing_a2,X9),X0)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X9)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_Graph_Ooutgoing_H__edges) ).
thf(f3422,plain,
spl155_96,
inference(avatar_split_clause,[],[f2296,f3420]) ).
thf(f2296,plain,
! [X0: product_prod_nat_nat > a,X1: set_nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),incoming_a2,X0),X1)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) ),
inference(definition_unfolding,[],[f1853,f1656]) ).
thf(f1853,plain,
! [X0: product_prod_nat_nat > a,X1: set_nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),incoming_a2,X0),X1)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) ),
inference(cnf_transformation,[],[f721]) ).
thf(f721,plain,
! [X0: product_prod_nat_nat > a,X1: set_nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),incoming_a2,X0),X1)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) ),
inference(fool_elimination,[],[f720]) ).
thf(f720,plain,
! [X0: product_prod_nat_nat > a,X1: set_nat] : vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),incoming_a2,X0),X1)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)),
inference(rectify,[],[f143]) ).
thf(f143,axiom,
! [X9: product_prod_nat_nat > a,X0: set_nat] : vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_nat,set_Pr1986765409at_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(set_nat,set_Pr1986765409at_nat),incoming_a2,X9),X0)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X9)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_Graph_Oincoming_H__edges) ).
thf(f3418,plain,
spl155_95,
inference(avatar_split_clause,[],[f2295,f3416]) ).
thf(f2295,plain,
! [X0: product_prod_nat_nat > a,X1: nat] : ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),adjacent_nodes_a,X0),X1)),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0)) ),
inference(definition_unfolding,[],[f1852,f1650]) ).
thf(f1852,plain,
! [X0: product_prod_nat_nat > a,X1: nat] : ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),adjacent_nodes_a,X0),X1)),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0)) ),
inference(cnf_transformation,[],[f719]) ).
thf(f719,plain,
! [X0: product_prod_nat_nat > a,X1: nat] : ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),adjacent_nodes_a,X0),X1)),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0)) ),
inference(fool_elimination,[],[f718]) ).
thf(f718,plain,
! [X0: product_prod_nat_nat > a,X1: nat] : vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),adjacent_nodes_a,X0),X1)),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X0)),
inference(rectify,[],[f184]) ).
thf(f184,axiom,
! [X9: product_prod_nat_nat > a,X1: nat] : vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),adjacent_nodes_a,X9),X1)),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,X9)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_Graph_Oadjacent__nodes__ss__V) ).
thf(f3396,plain,
spl155_94,
inference(avatar_split_clause,[],[f2201,f3394]) ).
thf(f2201,plain,
! [X0: set_Pr1986765409at_nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0)),X1) )
| ( $true = vAPP(nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(nat,$o),sP1,X0),X1) ) ),
inference(definition_unfolding,[],[f1750,f1646]) ).
thf(f1750,plain,
! [X0: set_Pr1986765409at_nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0)),X1) )
| ( $true = vAPP(nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(nat,$o),sP1,X0),X1) ) ),
inference(cnf_transformation,[],[f1431]) ).
thf(f1431,plain,
! [X0: set_Pr1986765409at_nat,X1: nat] :
( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0)),X1) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) ) )
| ( $true = vAPP(nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(nat,$o),sP1,X0),X1) ) ),
inference(definition_folding,[],[f1105,f1430]) ).
thf(f1105,plain,
! [X0: set_Pr1986765409at_nat,X1: nat] :
( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0)),X1) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) ) )
| ? [X2: set_Pr1986765409at_nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X2)),X1) )
& ( vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X2) = $true )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X2),X0) ) ) ),
inference(flattening,[],[f1104]) ).
thf(f1104,plain,
! [X0: set_Pr1986765409at_nat,X1: nat] :
( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0)),X1) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) ) )
| ? [X2: set_Pr1986765409at_nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X2)),X1) )
& ( vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X2) = $true )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X2),X0) ) ) ),
inference(ennf_transformation,[],[f551]) ).
thf(f551,plain,
! [X0: set_Pr1986765409at_nat,X1: nat] :
( ! [X2: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X2),X0) )
=> ( ( vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X2) = $true )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X2)),X1) ) ) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0)),X1) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) ) ) ),
inference(fool_elimination,[],[f550]) ).
thf(f550,plain,
! [X0: set_Pr1986765409at_nat,X1: nat] :
( ! [X2: set_Pr1986765409at_nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X2),X0)
=> ( vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X2)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X2)),X1) ) )
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X0)),X1)
& vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) ) ),
inference(rectify,[],[f335]) ).
thf(f335,axiom,
! [X38: set_Pr1986765409at_nat,X30: nat] :
( ! [X50: set_Pr1986765409at_nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X50),X38)
=> ( vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X50)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X50)),X30) ) )
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X38)),X30)
& vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X38) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_334_finite__if__finite__subsets__card__bdd) ).
thf(f3392,plain,
( spl155_93
| ~ spl155_67
| ~ spl155_84 ),
inference(avatar_split_clause,[],[f3317,f3281,f3205,f3390]) ).
thf(f3390,plain,
( spl155_93
<=> ! [X0: set_nat] : ( vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_93])]) ).
thf(f3205,plain,
( spl155_67
<=> ! [X0: set_nat] : ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_67])]) ).
thf(f3317,plain,
( ! [X0: set_nat] : ( vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X0) = X0 )
| ~ spl155_67
| ~ spl155_84 ),
inference(trivial_inequality_removal,[],[f3310]) ).
thf(f3310,plain,
( ! [X0: set_nat] :
( ( $true != $true )
| ( vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X0) = X0 ) )
| ~ spl155_67
| ~ spl155_84 ),
inference(superposition,[],[f3282,f3206]) ).
thf(f3206,plain,
( ! [X0: set_nat] : ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),X0) )
| ~ spl155_67 ),
inference(avatar_component_clause,[],[f3205]) ).
thf(f3388,plain,
spl155_92,
inference(avatar_split_clause,[],[f2193,f3386]) ).
thf(f2193,plain,
! [X0: set_nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(set_nat,nat,finite_card_nat,X0)),X1) )
| ( $true = vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,X0),X1) ) ),
inference(definition_unfolding,[],[f1741,f1646]) ).
thf(f1741,plain,
! [X0: set_nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(set_nat,nat,finite_card_nat,X0)),X1) )
| ( $true = vAPP(nat,$o,vAPP(set_nat,sTfun(nat,$o),sP0,X0),X1) ) ),
inference(cnf_transformation,[],[f1429]) ).
thf(f3384,plain,
spl155_91,
inference(avatar_split_clause,[],[f2184,f3382]) ).
thf(f2184,plain,
! [X0: set_Pr1986765409at_nat,X1: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sK11,X1),X0)),X0) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) ) ),
inference(definition_unfolding,[],[f1731,f1656]) ).
thf(f1731,plain,
! [X0: set_Pr1986765409at_nat,X1: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sK11,X1),X0)),X0) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) ) ),
inference(cnf_transformation,[],[f1448]) ).
thf(f1448,plain,
! [X0: set_Pr1986765409at_nat,X1: nat] :
( ( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sK11,X1),X0)),X0) )
& ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sK11,X1),X0)) = X1 )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sK11,X1),X0)) ) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f1096,f1447]) ).
thf(f1447,plain,
! [X0: set_Pr1986765409at_nat,X1: nat] :
( ? [X2: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X2),X0) )
& ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X2) = X1 )
& ( vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X2) = $true ) )
=> ( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sK11,X1),X0)),X0) )
& ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sK11,X1),X0)) = X1 )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sK11,X1),X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1096,plain,
! [X0: set_Pr1986765409at_nat,X1: nat] :
( ? [X2: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X2),X0) )
& ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X2) = X1 )
& ( vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X2) = $true ) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) ) ),
inference(ennf_transformation,[],[f1042]) ).
thf(f1042,plain,
! [X0: set_Pr1986765409at_nat,X1: nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) )
=> ? [X2: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X2),X0) )
& ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X2) = X1 )
& ( vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X2) = $true ) ) ),
inference(flattening,[],[f537]) ).
thf(f537,plain,
! [X0: set_Pr1986765409at_nat,X1: nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) )
=> ? [X2: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X2),X0) )
& ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X2) = X1 )
& ( vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X2) = $true ) ) ),
inference(fool_elimination,[],[f536]) ).
thf(f536,plain,
! [X0: set_Pr1986765409at_nat,X1: nat] :
( ~ vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0)
=> ? [X2: set_Pr1986765409at_nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X2),X0)
& ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X2) = X1 )
& vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X2) ) ),
inference(rectify,[],[f331]) ).
thf(f331,axiom,
! [X2: set_Pr1986765409at_nat,X48: nat] :
( ~ vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X2)
=> ? [X49: set_Pr1986765409at_nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X49),X2)
& ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,X49) = X48 )
& vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X49) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_330_infinite__arbitrarily__large) ).
thf(f3369,plain,
spl155_90,
inference(avatar_split_clause,[],[f2222,f3367]) ).
thf(f2222,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X1) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X1),X0) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) ) ),
inference(definition_unfolding,[],[f1775,f1656]) ).
thf(f1775,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X1) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X1),X0) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) ) ),
inference(cnf_transformation,[],[f1131]) ).
thf(f1131,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X1) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X1),X0) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) ) ),
inference(flattening,[],[f1130]) ).
thf(f1130,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X1) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X1),X0) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) ) ),
inference(ennf_transformation,[],[f577]) ).
thf(f577,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) )
=> ( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X1),X0) )
=> ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X1) ) ) ),
inference(fool_elimination,[],[f576]) ).
thf(f576,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0)
=> ( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X1),X0)
=> vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X1) ) ),
inference(rectify,[],[f321]) ).
thf(f321,axiom,
! [X3: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat] :
( vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X3)
=> ( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X2),X3)
=> vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_320_rev__finite__subset) ).
thf(f3303,plain,
spl155_89,
inference(avatar_split_clause,[],[f2253,f3301]) ).
thf(f2253,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1) = X0 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X1) ) ),
inference(definition_unfolding,[],[f1806,f1656]) ).
thf(f1806,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1) = X0 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1172]) ).
thf(f1172,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1) = X0 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1) ) ),
inference(ennf_transformation,[],[f639]) ).
thf(f639,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1) )
=> ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1) = X0 ) ),
inference(fool_elimination,[],[f638]) ).
thf(f638,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1)
=> ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1) = X0 ) ),
inference(rectify,[],[f279]) ).
thf(f279,axiom,
! [X13: set_Pr1986765409at_nat,X12: set_Pr1986765409at_nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X13),X12)
=> ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X13),X12) = X13 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_278_inf_Oabsorb1) ).
thf(f3299,plain,
spl155_88,
inference(avatar_split_clause,[],[f2252,f3297]) ).
thf(f2252,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),X0) = X0 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X1) ) ),
inference(definition_unfolding,[],[f1805,f1656]) ).
thf(f1805,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),X0) = X0 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1171]) ).
thf(f1171,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),X0) = X0 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1) ) ),
inference(ennf_transformation,[],[f637]) ).
thf(f637,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1) )
=> ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),X0) = X0 ) ),
inference(fool_elimination,[],[f636]) ).
thf(f636,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1)
=> ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),X0) = X0 ) ),
inference(rectify,[],[f276]) ).
thf(f276,axiom,
! [X12: set_Pr1986765409at_nat,X13: set_Pr1986765409at_nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X12),X13)
=> ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X13),X12) = X12 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_275_inf_Oabsorb2) ).
thf(f3295,plain,
spl155_87,
inference(avatar_split_clause,[],[f2246,f3293]) ).
thf(f2246,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X1),X0) = X0 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),X1) ) ),
inference(definition_unfolding,[],[f1799,f1646]) ).
thf(f1799,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X1),X0) = X0 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1162]) ).
thf(f1162,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X1),X0) = X0 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(ennf_transformation,[],[f625]) ).
thf(f625,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X1),X0) = X0 ) ),
inference(fool_elimination,[],[f624]) ).
thf(f624,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1)
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X1),X0) = X0 ) ),
inference(rectify,[],[f278]) ).
thf(f278,axiom,
! [X12: nat,X13: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X12),X13)
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X13),X12) = X12 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_277_inf_Oabsorb2) ).
thf(f3291,plain,
spl155_86,
inference(avatar_split_clause,[],[f2243,f3289]) ).
thf(f2243,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X1) = X0 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),X1) ) ),
inference(definition_unfolding,[],[f1796,f1646]) ).
thf(f1796,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X1) = X0 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1159]) ).
thf(f1159,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X1) = X0 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(ennf_transformation,[],[f619]) ).
thf(f619,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X1) = X0 ) ),
inference(fool_elimination,[],[f618]) ).
thf(f618,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1)
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X1) = X0 ) ),
inference(rectify,[],[f275]) ).
thf(f275,axiom,
! [X5: nat,X21: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X5),X21)
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X5),X21) = X5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_274_inf__absorb1) ).
thf(f3287,plain,
spl155_85,
inference(avatar_split_clause,[],[f2230,f3285]) ).
thf(f2230,plain,
! [X0: set_nat,X1: set_nat] :
( ( vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X1) = X0 )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),X1) ) ),
inference(definition_unfolding,[],[f1783,f1650]) ).
thf(f1783,plain,
! [X0: set_nat,X1: set_nat] :
( ( vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X1) = X0 )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1140]) ).
thf(f1140,plain,
! [X0: set_nat,X1: set_nat] :
( ( vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X1) = X0 )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1) ) ),
inference(ennf_transformation,[],[f593]) ).
thf(f593,plain,
! [X0: set_nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1) )
=> ( vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X1) = X0 ) ),
inference(fool_elimination,[],[f592]) ).
thf(f592,plain,
! [X0: set_nat,X1: set_nat] :
( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1)
=> ( vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X1) = X0 ) ),
inference(rectify,[],[f274]) ).
thf(f274,axiom,
! [X5: set_nat,X21: set_nat] :
( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X5),X21)
=> ( vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X5),X21) = X5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_273_inf__absorb1) ).
thf(f3283,plain,
spl155_84,
inference(avatar_split_clause,[],[f2229,f3281]) ).
thf(f2229,plain,
! [X0: set_nat,X1: set_nat] :
( ( vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),X0) = X0 )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),X1) ) ),
inference(definition_unfolding,[],[f1782,f1650]) ).
thf(f1782,plain,
! [X0: set_nat,X1: set_nat] :
( ( vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),X0) = X0 )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1139]) ).
thf(f1139,plain,
! [X0: set_nat,X1: set_nat] :
( ( vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),X0) = X0 )
| ( $true != vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1) ) ),
inference(ennf_transformation,[],[f591]) ).
thf(f591,plain,
! [X0: set_nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1) )
=> ( vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),X0) = X0 ) ),
inference(fool_elimination,[],[f590]) ).
thf(f590,plain,
! [X0: set_nat,X1: set_nat] :
( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1)
=> ( vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),X0) = X0 ) ),
inference(rectify,[],[f271]) ).
thf(f271,axiom,
! [X21: set_nat,X5: set_nat] :
( vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X21),X5)
=> ( vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X5),X21) = X21 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_270_inf__absorb2) ).
thf(f3279,plain,
spl155_83,
inference(avatar_split_clause,[],[f2178,f3277]) ).
thf(f3277,plain,
( spl155_83
<=> ! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X1) )
| ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1) != X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_83])]) ).
thf(f2178,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X1) )
| ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1) != X0 ) ),
inference(definition_unfolding,[],[f1721,f1656]) ).
thf(f1721,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1) )
| ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1) != X0 ) ),
inference(cnf_transformation,[],[f1092]) ).
thf(f1092,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1) )
| ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1) != X0 ) ),
inference(ennf_transformation,[],[f529]) ).
thf(f529,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1) = X0 )
=> ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1) ) ),
inference(fool_elimination,[],[f528]) ).
thf(f528,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1) = X0 )
=> vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X1) ),
inference(rectify,[],[f288]) ).
thf(f288,axiom,
! [X13: set_Pr1986765409at_nat,X12: set_Pr1986765409at_nat] :
( ( vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X13),X12) = X13 )
=> vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X13),X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_287_inf_OorderI) ).
thf(f3275,plain,
( spl155_82
| ~ spl155_4
| ~ spl155_11 ),
inference(avatar_split_clause,[],[f2839,f2814,f2775,f3273]) ).
thf(f3273,plain,
( spl155_82
<=> ! [X0: set_Pr1986765409at_nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,c))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_82])]) ).
thf(f2839,plain,
( ! [X0: set_Pr1986765409at_nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,c))) )
| ~ spl155_4
| ~ spl155_11 ),
inference(trivial_inequality_removal,[],[f2834]) ).
thf(f2834,plain,
( ! [X0: set_Pr1986765409at_nat] :
( ( $true != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,c))) ) )
| ~ spl155_4
| ~ spl155_11 ),
inference(superposition,[],[f2815,f2777]) ).
thf(f3271,plain,
spl155_81,
inference(avatar_split_clause,[],[f2177,f3269]) ).
thf(f3269,plain,
( spl155_81
<=> ! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),X1) )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X1) != X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_81])]) ).
thf(f2177,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),X1) )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X1) != X0 ) ),
inference(definition_unfolding,[],[f1720,f1646]) ).
thf(f1720,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X1) != X0 ) ),
inference(cnf_transformation,[],[f1091]) ).
thf(f1091,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X1) != X0 ) ),
inference(ennf_transformation,[],[f527]) ).
thf(f527,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X1) = X0 )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ),
inference(fool_elimination,[],[f526]) ).
thf(f526,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X1) = X0 )
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ),
inference(rectify,[],[f290]) ).
thf(f290,axiom,
! [X13: nat,X12: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X13),X12) = X13 )
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X13),X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_289_inf_OorderI) ).
thf(f3267,plain,
spl155_80,
inference(avatar_split_clause,[],[f2176,f3265]) ).
thf(f3265,plain,
( spl155_80
<=> ! [X0: set_nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),X1) )
| ( vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X1) != X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_80])]) ).
thf(f2176,plain,
! [X0: set_nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),X1) )
| ( vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X1) != X0 ) ),
inference(definition_unfolding,[],[f1719,f1650]) ).
thf(f1719,plain,
! [X0: set_nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1) )
| ( vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X1) != X0 ) ),
inference(cnf_transformation,[],[f1090]) ).
thf(f1090,plain,
! [X0: set_nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1) )
| ( vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X1) != X0 ) ),
inference(ennf_transformation,[],[f525]) ).
thf(f525,plain,
! [X0: set_nat,X1: set_nat] :
( ( vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X1) = X0 )
=> ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1) ) ),
inference(fool_elimination,[],[f524]) ).
thf(f524,plain,
! [X0: set_nat,X1: set_nat] :
( ( vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X1) = X0 )
=> vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X1) ),
inference(rectify,[],[f289]) ).
thf(f289,axiom,
! [X13: set_nat,X12: set_nat] :
( ( vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X13),X12) = X13 )
=> vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X13),X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_288_inf_OorderI) ).
thf(f3263,plain,
spl155_79,
inference(avatar_split_clause,[],[f2485,f3260]) ).
thf(f2485,plain,
$true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,c)),
inference(definition_unfolding,[],[f2093,f1656]) ).
thf(f2093,plain,
vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,c)) = $true,
inference(cnf_transformation,[],[f1027]) ).
thf(f1027,plain,
vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,c)) = $true,
inference(fool_elimination,[],[f1026]) ).
thf(f1026,plain,
vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,c)),
inference(rectify,[],[f6]) ).
thf(f6,axiom,
vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_E__ss__uE) ).
thf(f3254,plain,
( spl155_78
| ~ spl155_5
| ~ spl155_11 ),
inference(avatar_split_clause,[],[f2838,f2814,f2780,f3252]) ).
thf(f3252,plain,
( spl155_78
<=> ! [X0: set_Pr1986765409at_nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_78])]) ).
thf(f2838,plain,
( ! [X0: set_Pr1986765409at_nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c))) )
| ~ spl155_5
| ~ spl155_11 ),
inference(trivial_inequality_removal,[],[f2835]) ).
thf(f2835,plain,
( ! [X0: set_Pr1986765409at_nat] :
( ( $true != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c))) ) )
| ~ spl155_5
| ~ spl155_11 ),
inference(superposition,[],[f2815,f2782]) ).
thf(f3250,plain,
spl155_77,
inference(avatar_split_clause,[],[f2288,f3248]) ).
thf(f2288,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1)),X1) ),
inference(definition_unfolding,[],[f1845,f1656]) ).
thf(f1845,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1)),X1) ),
inference(cnf_transformation,[],[f705]) ).
thf(f705,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1)),X1) ),
inference(fool_elimination,[],[f704]) ).
thf(f704,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] : vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1)),X1),
inference(rectify,[],[f318]) ).
thf(f318,axiom,
! [X5: set_Pr1986765409at_nat,X21: set_Pr1986765409at_nat] : vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X5),X21)),X21),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_317_inf__sup__ord_I2_J) ).
thf(f3246,plain,
spl155_76,
inference(avatar_split_clause,[],[f2287,f3244]) ).
thf(f2287,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1)),X0) ),
inference(definition_unfolding,[],[f1844,f1656]) ).
thf(f1844,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1)),X0) ),
inference(cnf_transformation,[],[f703]) ).
thf(f703,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1)),X0) ),
inference(fool_elimination,[],[f702]) ).
thf(f702,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] : vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1)),X0),
inference(rectify,[],[f315]) ).
thf(f315,axiom,
! [X5: set_Pr1986765409at_nat,X21: set_Pr1986765409at_nat] : vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X5),X21)),X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_314_inf__sup__ord_I1_J) ).
thf(f3242,plain,
spl155_75,
inference(avatar_split_clause,[],[f2282,f3240]) ).
thf(f2282,plain,
! [X0: nat,X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X1)),X0) ),
inference(definition_unfolding,[],[f1839,f1646]) ).
thf(f1839,plain,
! [X0: nat,X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X1)),X0) ),
inference(cnf_transformation,[],[f693]) ).
thf(f693,plain,
! [X0: nat,X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X1)),X0) ),
inference(fool_elimination,[],[f692]) ).
thf(f692,plain,
! [X0: nat,X1: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X1)),X0),
inference(rectify,[],[f317]) ).
thf(f317,axiom,
! [X5: nat,X21: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X5),X21)),X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_316_inf__sup__ord_I1_J) ).
thf(f3238,plain,
spl155_74,
inference(avatar_split_clause,[],[f2281,f3236]) ).
thf(f2281,plain,
! [X0: nat,X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X1)),X1) ),
inference(definition_unfolding,[],[f1838,f1646]) ).
thf(f1838,plain,
! [X0: nat,X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X1)),X1) ),
inference(cnf_transformation,[],[f691]) ).
thf(f691,plain,
! [X0: nat,X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X1)),X1) ),
inference(fool_elimination,[],[f690]) ).
thf(f690,plain,
! [X0: nat,X1: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X0),X1)),X1),
inference(rectify,[],[f254]) ).
thf(f254,axiom,
! [X13: nat,X12: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),inf_inf_nat,X13),X12)),X12),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_inf_Ocobounded2) ).
thf(f3234,plain,
spl155_73,
inference(avatar_split_clause,[],[f2274,f3232]) ).
thf(f2274,plain,
! [X0: set_nat,X1: set_nat] : ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X1)),X0) ),
inference(definition_unfolding,[],[f1831,f1650]) ).
thf(f1831,plain,
! [X0: set_nat,X1: set_nat] : ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X1)),X0) ),
inference(cnf_transformation,[],[f677]) ).
thf(f677,plain,
! [X0: set_nat,X1: set_nat] : ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X1)),X0) ),
inference(fool_elimination,[],[f676]) ).
thf(f676,plain,
! [X0: set_nat,X1: set_nat] : vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X1)),X0),
inference(rectify,[],[f173]) ).
thf(f173,axiom,
! [X2: set_nat,X3: set_nat] : vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X2),X3)),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_Int__lower1) ).
thf(f3230,plain,
spl155_72,
inference(avatar_split_clause,[],[f2273,f3228]) ).
thf(f2273,plain,
! [X0: set_nat,X1: set_nat] : ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X1)),X1) ),
inference(definition_unfolding,[],[f1830,f1650]) ).
thf(f1830,plain,
! [X0: set_nat,X1: set_nat] : ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X1)),X1) ),
inference(cnf_transformation,[],[f675]) ).
thf(f675,plain,
! [X0: set_nat,X1: set_nat] : ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X1)),X1) ),
inference(fool_elimination,[],[f674]) ).
thf(f674,plain,
! [X0: set_nat,X1: set_nat] : vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X0),X1)),X1),
inference(rectify,[],[f253]) ).
thf(f253,axiom,
! [X13: set_nat,X12: set_nat] : vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X13),X12)),X12),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_inf_Ocobounded2) ).
thf(f3226,plain,
spl155_71,
inference(avatar_split_clause,[],[f2484,f3223]) ).
thf(f2484,plain,
$true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),edges),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p)),
inference(definition_unfolding,[],[f2091,f1656]) ).
thf(f2091,plain,
vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,edges),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p)) = $true,
inference(cnf_transformation,[],[f1023]) ).
thf(f1023,plain,
vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,edges),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p)) = $true,
inference(fool_elimination,[],[f1022]) ).
thf(f1022,plain,
vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,edges),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p)),
inference(rectify,[],[f2]) ).
thf(f2,axiom,
vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,edges),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,p)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_SP__EDGES) ).
thf(f3219,plain,
( spl155_70
| ~ spl155_4
| ~ spl155_10 ),
inference(avatar_split_clause,[],[f2831,f2810,f2775,f3217]) ).
thf(f3217,plain,
( spl155_70
<=> ! [X0: set_Pr1986765409at_nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,c)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_70])]) ).
thf(f2831,plain,
( ! [X0: set_Pr1986765409at_nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,c)),X0)) )
| ~ spl155_4
| ~ spl155_10 ),
inference(trivial_inequality_removal,[],[f2826]) ).
thf(f2826,plain,
( ! [X0: set_Pr1986765409at_nat] :
( ( $true != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,c)),X0)) ) )
| ~ spl155_4
| ~ spl155_10 ),
inference(superposition,[],[f2811,f2777]) ).
thf(f3215,plain,
spl155_69,
inference(avatar_split_clause,[],[f2151,f3213]) ).
thf(f2151,plain,
! [X0: set_Pr1986765409at_nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),X0),X0) ),
inference(definition_unfolding,[],[f1691,f1656]) ).
thf(f1691,plain,
! [X0: set_Pr1986765409at_nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X0) ),
inference(cnf_transformation,[],[f477]) ).
thf(f477,plain,
! [X0: set_Pr1986765409at_nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X0) ),
inference(fool_elimination,[],[f476]) ).
thf(f476,plain,
! [X0: set_Pr1986765409at_nat] : vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X0),X0),
inference(rectify,[],[f14]) ).
thf(f14,axiom,
! [X5: set_Pr1986765409at_nat] : vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,X5),X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_order__refl) ).
thf(f3211,plain,
spl155_68,
inference(avatar_split_clause,[],[f2149,f3209]) ).
thf(f2149,plain,
! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),inf_inf_nat))),iCOMB),X0),X0) ),
inference(definition_unfolding,[],[f1689,f1646]) ).
thf(f1689,plain,
! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X0) ),
inference(cnf_transformation,[],[f473]) ).
thf(f473,plain,
! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X0) ),
inference(fool_elimination,[],[f472]) ).
thf(f472,plain,
! [X0: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X0),
inference(rectify,[],[f41]) ).
thf(f41,axiom,
! [X13: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X13),X13),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_dual__order_Orefl) ).
thf(f3207,plain,
spl155_67,
inference(avatar_split_clause,[],[f2146,f3205]) ).
thf(f2146,plain,
! [X0: set_nat] : ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),vAPP(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o)),vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o))),vAPP(sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),sTfun(sTfun(set_nat,sTfun(set_nat,set_nat)),sTfun(set_nat,sTfun(set_nat,sTfun(set_nat,$o)))),bCOMB,vAPP(sTfun(set_nat,sTfun(set_nat,$o)),sTfun(sTfun(set_nat,set_nat),sTfun(set_nat,sTfun(set_nat,$o))),bCOMB,vEQ(set_nat))),inf_inf_set_nat))),iCOMB),X0),X0) ),
inference(definition_unfolding,[],[f1686,f1650]) ).
thf(f1686,plain,
! [X0: set_nat] : ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X0) ),
inference(cnf_transformation,[],[f467]) ).
thf(f467,plain,
! [X0: set_nat] : ( $true = vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X0) ),
inference(fool_elimination,[],[f466]) ).
thf(f466,plain,
! [X0: set_nat] : vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X0),X0),
inference(rectify,[],[f124]) ).
thf(f124,axiom,
! [X2: set_nat] : vAPP(set_nat,$o,vAPP(set_nat,sTfun(set_nat,$o),ord_less_eq_set_nat,X2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_subset__refl) ).
thf(f3201,plain,
spl155_66,
inference(avatar_split_clause,[],[f2730,f3199]) ).
thf(f2730,plain,
! [X2: nat,X0: nat,X1: list_P559422087at_nat] :
( ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),sK33,X2),X1),X0)),vAPP(nat,list_P559422087at_nat,vAPP(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat)),sK34,X2),X1),X0)),X2) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X0),vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),sK33,X2),X1),X0))),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) )
| ( vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),sK32,X2),X1),X0) != X0 )
| ( nil_Pr1308055047at_nat = X1 )
| ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2) ) ),
inference(inner_rewriting,[],[f1885]) ).
thf(f1885,plain,
! [X2: nat,X0: nat,X1: list_P559422087at_nat] :
( ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),sK33,X2),X1),X0)),vAPP(nat,list_P559422087at_nat,vAPP(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat)),sK34,X2),X1),X0)),X2) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),sK32,X2),X1),X0)),vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),sK33,X2),X1),X0))),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) )
| ( vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),sK32,X2),X1),X0) != X0 )
| ( nil_Pr1308055047at_nat = X1 )
| ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2) ) ),
inference(cnf_transformation,[],[f1497]) ).
thf(f1497,plain,
! [X0: nat,X1: list_P559422087at_nat,X2: nat] :
( ( ( ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),sK33,X2),X1),X0)),vAPP(nat,list_P559422087at_nat,vAPP(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat)),sK34,X2),X1),X0)),X2) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),sK32,X2),X1),X0)),vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),sK33,X2),X1),X0))),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) )
| ( vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),sK32,X2),X1),X0) != X0 ) )
& ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),sK32,X2),X1),X0)),vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),sK33,X2),X1),X0))),vAPP(nat,list_P559422087at_nat,vAPP(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat)),sK34,X2),X1),X0)) = X1 ) )
| ( ( X0 != X2 )
& ( nil_Pr1308055047at_nat = X1 ) )
| ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK32,sK33,sK34])],[f1209,f1496]) ).
thf(f1496,plain,
! [X0: nat,X1: list_P559422087at_nat,X2: nat] :
( ? [X3: nat,X4: nat,X5: list_P559422087at_nat] :
( ( ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X4),X5),X2) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X3),X4)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) )
| ( X0 != X3 ) )
& ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X3),X4)),X5) = X1 ) )
=> ( ( ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),sK33,X2),X1),X0)),vAPP(nat,list_P559422087at_nat,vAPP(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat)),sK34,X2),X1),X0)),X2) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),sK32,X2),X1),X0)),vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),sK33,X2),X1),X0))),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) )
| ( vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),sK32,X2),X1),X0) != X0 ) )
& ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),sK32,X2),X1),X0)),vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),sK33,X2),X1),X0))),vAPP(nat,list_P559422087at_nat,vAPP(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat)),sK34,X2),X1),X0)) = X1 ) ) ),
introduced(choice_axiom,[]) ).
thf(f1209,plain,
! [X0: nat,X1: list_P559422087at_nat,X2: nat] :
( ? [X3: nat,X4: nat,X5: list_P559422087at_nat] :
( ( ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X4),X5),X2) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X3),X4)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) )
| ( X0 != X3 ) )
& ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X3),X4)),X5) = X1 ) )
| ( ( X0 != X2 )
& ( nil_Pr1308055047at_nat = X1 ) )
| ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2) ) ),
inference(flattening,[],[f1208]) ).
thf(f1208,plain,
! [X0: nat,X1: list_P559422087at_nat,X2: nat] :
( ? [X3: nat,X4: nat,X5: list_P559422087at_nat] :
( ( ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X4),X5),X2) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X3),X4)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) )
| ( X0 != X3 ) )
& ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X3),X4)),X5) = X1 ) )
| ( ( X0 != X2 )
& ( nil_Pr1308055047at_nat = X1 ) )
| ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2) ) ),
inference(ennf_transformation,[],[f1051]) ).
thf(f1051,plain,
! [X0: nat,X1: list_P559422087at_nat,X2: nat] :
( ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2) )
=> ( ( ( nil_Pr1308055047at_nat = X1 )
=> ( X0 = X2 ) )
=> ~ ! [X3: nat,X4: nat,X5: list_P559422087at_nat] :
( ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X3),X4)),X5) = X1 )
=> ( ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X4),X5),X2) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X3),X4)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) )
& ( X0 = X3 ) ) ) ) ),
inference(flattening,[],[f759]) ).
thf(f759,plain,
! [X0: nat,X1: list_P559422087at_nat,X2: nat] :
( ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2) )
=> ( ( ( nil_Pr1308055047at_nat = X1 )
=> ( X0 = X2 ) )
=> ~ ! [X3: nat,X4: nat,X5: list_P559422087at_nat] :
( ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X3),X4)),X5) = X1 )
=> ( ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X4),X5),X2) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X3),X4)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) )
& ( X0 = X3 ) ) ) ) ),
inference(fool_elimination,[],[f758]) ).
thf(f758,plain,
! [X0: nat,X1: list_P559422087at_nat,X2: nat] :
( ~ vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2)
=> ( ( ( nil_Pr1308055047at_nat = X1 )
=> ( X0 = X2 ) )
=> ~ ! [X3: nat,X4: nat,X5: list_P559422087at_nat] :
( ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X3),X4)),X5) = X1 )
=> ( vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X4),X5),X2)
& vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X3),X4)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c))
& ( X0 = X3 ) ) ) ) ),
inference(rectify,[],[f348]) ).
thf(f348,axiom,
! [X5: nat,X65: list_P559422087at_nat,X66: nat] :
( ~ vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X5),X65),X66)
=> ( ( ( nil_Pr1308055047at_nat = X65 )
=> ( X5 = X66 ) )
=> ~ ! [X4: nat,X26: nat,X67: list_P559422087at_nat] :
( ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X4),X26)),X67) = X65 )
=> ( vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X26),X67),X66)
& vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X4),X26)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c))
& ( X4 = X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_347_isPath_Oelims_I3_J) ).
thf(f3195,plain,
spl155_65,
inference(avatar_split_clause,[],[f2729,f3193]) ).
thf(f2729,plain,
! [X2: nat,X1: list_P559422087at_nat] :
( ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),sK33,X2),X1),X2)),vAPP(nat,list_P559422087at_nat,vAPP(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat)),sK34,X2),X1),X2)),X2) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X2),vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),sK33,X2),X1),X2))),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) )
| ( vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),sK32,X2),X1),X2) != X2 )
| ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X2),X1),X2) ) ),
inference(inner_rewriting,[],[f2502]) ).
thf(f2502,plain,
! [X2: nat,X1: list_P559422087at_nat] :
( ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),sK33,X2),X1),X2)),vAPP(nat,list_P559422087at_nat,vAPP(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat)),sK34,X2),X1),X2)),X2) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),sK32,X2),X1),X2)),vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),sK33,X2),X1),X2))),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) )
| ( vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),sK32,X2),X1),X2) != X2 )
| ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X2),X1),X2) ) ),
inference(equality_resolution,[],[f1886]) ).
thf(f1886,plain,
! [X2: nat,X0: nat,X1: list_P559422087at_nat] :
( ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),sK33,X2),X1),X0)),vAPP(nat,list_P559422087at_nat,vAPP(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat)),sK34,X2),X1),X0)),X2) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),sK32,X2),X1),X0)),vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),sK33,X2),X1),X0))),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) )
| ( vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),sK32,X2),X1),X0) != X0 )
| ( X0 != X2 )
| ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2) ) ),
inference(cnf_transformation,[],[f1497]) ).
thf(f3189,plain,
spl155_64,
inference(avatar_split_clause,[],[f2009,f3187]) ).
thf(f2009,plain,
! [X2: list_P559422087at_nat,X3: nat,X0: nat > list_P559422087at_nat > nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),X0,X1),X2),X3) )
| ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),X0,vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),nat,sK88,X0)),vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),nat,sK89,X0)),vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),nat,sK90,X0))),vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),list_P559422087at_nat,sK91,X0))),vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),nat,sK92,X0)) )
| ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),X0,vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),nat,sK93,X0)),nil_Pr1308055047at_nat),vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),nat,sK94,X0)) ) ),
inference(cnf_transformation,[],[f1552]) ).
thf(f1552,plain,
! [X0: nat > list_P559422087at_nat > nat > $o,X1: nat,X2: list_P559422087at_nat,X3: nat] :
( ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),X0,X1),X2),X3) )
| ( ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),X0,vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),nat,sK88,X0)),vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),nat,sK89,X0)),vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),nat,sK90,X0))),vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),list_P559422087at_nat,sK91,X0))),vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),nat,sK92,X0)) )
& ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),X0,vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),nat,sK90,X0)),vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),list_P559422087at_nat,sK91,X0)),vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),nat,sK92,X0)) ) )
| ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),X0,vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),nat,sK93,X0)),nil_Pr1308055047at_nat),vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),nat,sK94,X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK88,sK89,sK90,sK91,sK92,sK93,sK94])],[f1549,f1551,f1550]) ).
thf(f1550,plain,
! [X0: nat > list_P559422087at_nat > nat > $o] :
( ? [X4: nat,X5: nat,X6: nat,X7: list_P559422087at_nat,X8: nat] :
( ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),X0,X4),vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X5),X6)),X7)),X8) )
& ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),X0,X6),X7),X8) ) )
=> ( ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),X0,vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),nat,sK88,X0)),vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),nat,sK89,X0)),vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),nat,sK90,X0))),vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),list_P559422087at_nat,sK91,X0))),vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),nat,sK92,X0)) )
& ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),X0,vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),nat,sK90,X0)),vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),list_P559422087at_nat,sK91,X0)),vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),nat,sK92,X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1551,plain,
! [X0: nat > list_P559422087at_nat > nat > $o] :
( ? [X9: nat,X10: nat] : ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),X0,X9),nil_Pr1308055047at_nat),X10) )
=> ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),X0,vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),nat,sK93,X0)),nil_Pr1308055047at_nat),vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),nat,sK94,X0)) ) ),
introduced(choice_axiom,[]) ).
thf(f1549,plain,
! [X0: nat > list_P559422087at_nat > nat > $o,X1: nat,X2: list_P559422087at_nat,X3: nat] :
( ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),X0,X1),X2),X3) )
| ? [X4: nat,X5: nat,X6: nat,X7: list_P559422087at_nat,X8: nat] :
( ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),X0,X4),vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X5),X6)),X7)),X8) )
& ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),X0,X6),X7),X8) ) )
| ? [X9: nat,X10: nat] : ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),X0,X9),nil_Pr1308055047at_nat),X10) ) ),
inference(rectify,[],[f1340]) ).
thf(f1340,plain,
! [X0: nat > list_P559422087at_nat > nat > $o,X1: nat,X2: list_P559422087at_nat,X3: nat] :
( ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),X0,X1),X2),X3) )
| ? [X6: nat,X7: nat,X8: nat,X9: list_P559422087at_nat,X10: nat] :
( ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),X0,X6),vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X7),X8)),X9)),X10) )
& ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),X0,X8),X9),X10) ) )
| ? [X4: nat,X5: nat] : ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),X0,X4),nil_Pr1308055047at_nat),X5) ) ),
inference(flattening,[],[f1339]) ).
thf(f1339,plain,
! [X0: nat > list_P559422087at_nat > nat > $o,X1: nat,X2: list_P559422087at_nat,X3: nat] :
( ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),X0,X1),X2),X3) )
| ? [X6: nat,X7: nat,X8: nat,X9: list_P559422087at_nat,X10: nat] :
( ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),X0,X6),vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X7),X8)),X9)),X10) )
& ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),X0,X8),X9),X10) ) )
| ? [X4: nat,X5: nat] : ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),X0,X4),nil_Pr1308055047at_nat),X5) ) ),
inference(ennf_transformation,[],[f921]) ).
thf(f921,plain,
! [X0: nat > list_P559422087at_nat > nat > $o,X1: nat,X2: list_P559422087at_nat,X3: nat] :
( ! [X4: nat,X5: nat] : ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),X0,X4),nil_Pr1308055047at_nat),X5) )
=> ( ! [X6: nat,X7: nat,X8: nat,X9: list_P559422087at_nat,X10: nat] :
( ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),X0,X8),X9),X10) )
=> ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),X0,X6),vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X7),X8)),X9)),X10) ) )
=> ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),X0,X1),X2),X3) ) ) ),
inference(fool_elimination,[],[f920]) ).
thf(f920,plain,
! [X0: nat > list_P559422087at_nat > nat > $o,X1: nat,X2: list_P559422087at_nat,X3: nat] :
( ! [X4: nat,X5: nat] : vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),X0,X4),nil_Pr1308055047at_nat),X5)
=> ( ! [X6: nat,X7: nat,X8: nat,X9: list_P559422087at_nat,X10: nat] :
( vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),X0,X8),X9),X10)
=> vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),X0,X6),vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X7),X8)),X9)),X10) )
=> vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),X0,X1),X2),X3) ) ),
inference(rectify,[],[f353]) ).
thf(f353,axiom,
! [X18: nat > list_P559422087at_nat > nat > $o,X70: nat,X71: list_P559422087at_nat,X72: nat] :
( ! [X69: nat,X73: nat] : vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),X18,X69),nil_Pr1308055047at_nat),X73)
=> ( ! [X69: nat,X4: nat,X26: nat,X67: list_P559422087at_nat,X74: nat] :
( vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),X18,X26),X67),X74)
=> vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),X18,X69),vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X4),X26)),X67)),X74) )
=> vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),X18,X70),X71),X72) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_352_Graph_OisPath_Oinduct) ).
thf(f3185,plain,
( spl155_63
| ~ spl155_5
| ~ spl155_10 ),
inference(avatar_split_clause,[],[f2830,f2810,f2780,f3183]) ).
thf(f3183,plain,
( spl155_63
<=> ! [X0: set_Pr1986765409at_nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_63])]) ).
thf(f2830,plain,
( ! [X0: set_Pr1986765409at_nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),X0)) )
| ~ spl155_5
| ~ spl155_10 ),
inference(trivial_inequality_removal,[],[f2827]) ).
thf(f2827,plain,
( ! [X0: set_Pr1986765409at_nat] :
( ( $true != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),X0)) ) )
| ~ spl155_5
| ~ spl155_10 ),
inference(superposition,[],[f2811,f2782]) ).
thf(f3179,plain,
spl155_62,
inference(avatar_split_clause,[],[f2008,f3177]) ).
thf(f2008,plain,
! [X2: list_P559422087at_nat,X3: nat,X0: nat > list_P559422087at_nat > nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),X0,X1),X2),X3) )
| ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),X0,vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),nat,sK90,X0)),vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),list_P559422087at_nat,sK91,X0)),vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),nat,sK92,X0)) )
| ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),X0,vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),nat,sK93,X0)),nil_Pr1308055047at_nat),vAPP(sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),nat,sK94,X0)) ) ),
inference(cnf_transformation,[],[f1552]) ).
thf(f3175,plain,
spl155_61,
inference(avatar_split_clause,[],[f1883,f3173]) ).
thf(f3173,plain,
( spl155_61
<=> ! [X2: nat,X0: nat,X1: list_P559422087at_nat] :
( ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),sK32,X2),X1),X0)),vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),sK33,X2),X1),X0))),vAPP(nat,list_P559422087at_nat,vAPP(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat)),sK34,X2),X1),X0)) = X1 )
| ( nil_Pr1308055047at_nat = X1 )
| ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_61])]) ).
thf(f1883,plain,
! [X2: nat,X0: nat,X1: list_P559422087at_nat] :
( ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),sK32,X2),X1),X0)),vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),sK33,X2),X1),X0))),vAPP(nat,list_P559422087at_nat,vAPP(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat)),sK34,X2),X1),X0)) = X1 )
| ( nil_Pr1308055047at_nat = X1 )
| ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2) ) ),
inference(cnf_transformation,[],[f1497]) ).
thf(f3171,plain,
spl155_60,
inference(avatar_split_clause,[],[f2503,f3169]) ).
thf(f3169,plain,
( spl155_60
<=> ! [X2: nat,X1: list_P559422087at_nat] :
( ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),sK32,X2),X1),X2)),vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),sK33,X2),X1),X2))),vAPP(nat,list_P559422087at_nat,vAPP(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat)),sK34,X2),X1),X2)) = X1 )
| ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X2),X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_60])]) ).
thf(f2503,plain,
! [X2: nat,X1: list_P559422087at_nat] :
( ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),sK32,X2),X1),X2)),vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),sK33,X2),X1),X2))),vAPP(nat,list_P559422087at_nat,vAPP(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat)),sK34,X2),X1),X2)) = X1 )
| ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X2),X1),X2) ) ),
inference(equality_resolution,[],[f1884]) ).
thf(f1884,plain,
! [X2: nat,X0: nat,X1: list_P559422087at_nat] :
( ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),sK32,X2),X1),X0)),vAPP(nat,nat,vAPP(list_P559422087at_nat,sTfun(nat,nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,nat)),sK33,X2),X1),X0))),vAPP(nat,list_P559422087at_nat,vAPP(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,list_P559422087at_nat)),sK34,X2),X1),X0)) = X1 )
| ( X0 != X2 )
| ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2) ) ),
inference(cnf_transformation,[],[f1497]) ).
thf(f3159,plain,
( spl155_59
| ~ spl155_4
| ~ spl155_6 ),
inference(avatar_split_clause,[],[f2794,f2785,f2775,f3156]) ).
thf(f3156,plain,
( spl155_59
<=> ( vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,c) = vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,vAPP(set_Pr1986765409at_nat,list_P559422087at_nat,sK9,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,c))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_59])]) ).
thf(f2794,plain,
( ( vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,c) = vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,vAPP(set_Pr1986765409at_nat,list_P559422087at_nat,sK9,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,c))) )
| ~ spl155_4
| ~ spl155_6 ),
inference(trivial_inequality_removal,[],[f2789]) ).
thf(f2789,plain,
( ( $true != $true )
| ( vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,c) = vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,vAPP(set_Pr1986765409at_nat,list_P559422087at_nat,sK9,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,c))) )
| ~ spl155_4
| ~ spl155_6 ),
inference(superposition,[],[f2786,f2777]) ).
thf(f3154,plain,
spl155_58,
inference(avatar_split_clause,[],[f2085,f3152]) ).
thf(f2085,plain,
! [X2: list_P559422087at_nat,X3: nat,X0: product_prod_nat_nat > a,X1: nat,X4: nat,X5: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(list_P559422087at_nat,nat,vAPP(nat,sTfun(list_P559422087at_nat,nat),sK154,X4),X2)),X4)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X2)) )
| ( X1 = X4 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X4),X5)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X2)) )
| ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,X0),X1),X2),X3) ) ),
inference(cnf_transformation,[],[f1618]) ).
thf(f1618,plain,
! [X0: product_prod_nat_nat > a,X1: nat,X2: list_P559422087at_nat,X3: nat,X4: nat,X5: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(list_P559422087at_nat,nat,vAPP(nat,sTfun(list_P559422087at_nat,nat),sK154,X4),X2)),X4)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X2)) )
| ( X1 = X4 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X4),X5)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X2)) )
| ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,X0),X1),X2),X3) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK154])],[f1427,f1617]) ).
thf(f1617,plain,
! [X2: list_P559422087at_nat,X4: nat] :
( ? [X6: nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X6),X4)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X2)) )
=> ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(list_P559422087at_nat,nat,vAPP(nat,sTfun(list_P559422087at_nat,nat),sK154,X4),X2)),X4)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X2)) ) ),
introduced(choice_axiom,[]) ).
thf(f1427,plain,
! [X0: product_prod_nat_nat > a,X1: nat,X2: list_P559422087at_nat,X3: nat,X4: nat,X5: nat] :
( ? [X6: nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X6),X4)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X2)) )
| ( X1 = X4 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X4),X5)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X2)) )
| ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,X0),X1),X2),X3) ) ),
inference(flattening,[],[f1426]) ).
thf(f1426,plain,
! [X0: product_prod_nat_nat > a,X1: nat,X2: list_P559422087at_nat,X3: nat,X4: nat,X5: nat] :
( ? [X6: nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X6),X4)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X2)) )
| ( X1 = X4 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X4),X5)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X2)) )
| ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,X0),X1),X2),X3) ) ),
inference(ennf_transformation,[],[f1011]) ).
thf(f1011,plain,
! [X0: product_prod_nat_nat > a,X1: nat,X2: list_P559422087at_nat,X3: nat,X4: nat,X5: nat] :
( ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,X0),X1),X2),X3) )
=> ( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X4),X5)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X2)) )
=> ( ( X1 != X4 )
=> ? [X6: nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X6),X4)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X2)) ) ) ) ),
inference(fool_elimination,[],[f1010]) ).
thf(f1010,plain,
! [X0: product_prod_nat_nat > a,X1: nat,X2: list_P559422087at_nat,X3: nat,X4: nat,X5: nat] :
( vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,X0),X1),X2),X3)
=> ( vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X4),X5)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X2))
=> ( ( X1 != X4 )
=> ? [X6: nat] : vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X6),X4)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X2)) ) ) ),
inference(rectify,[],[f186]) ).
thf(f186,axiom,
! [X9: product_prod_nat_nat > a,X1: nat,X6: list_P559422087at_nat,X7: nat,X33: nat,X34: nat] :
( vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,X9),X1),X6),X7)
=> ( vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X33),X34)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X6))
=> ( ( X1 != X33 )
=> ? [X36: nat] : vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X36),X33)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X6)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_Graph_OisPath__ex__edge1) ).
thf(f3150,plain,
spl155_57,
inference(avatar_split_clause,[],[f2084,f3148]) ).
thf(f2084,plain,
! [X2: list_P559422087at_nat,X3: nat,X0: product_prod_nat_nat > a,X1: nat,X4: nat,X5: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X5),vAPP(list_P559422087at_nat,nat,vAPP(nat,sTfun(list_P559422087at_nat,nat),sK153,X5),X2))),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X2)) )
| ( X3 = X5 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X4),X5)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X2)) )
| ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,X0),X1),X2),X3) ) ),
inference(cnf_transformation,[],[f1616]) ).
thf(f1616,plain,
! [X0: product_prod_nat_nat > a,X1: nat,X2: list_P559422087at_nat,X3: nat,X4: nat,X5: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X5),vAPP(list_P559422087at_nat,nat,vAPP(nat,sTfun(list_P559422087at_nat,nat),sK153,X5),X2))),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X2)) )
| ( X3 = X5 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X4),X5)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X2)) )
| ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,X0),X1),X2),X3) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK153])],[f1425,f1615]) ).
thf(f1615,plain,
! [X2: list_P559422087at_nat,X5: nat] :
( ? [X6: nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X5),X6)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X2)) )
=> ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X5),vAPP(list_P559422087at_nat,nat,vAPP(nat,sTfun(list_P559422087at_nat,nat),sK153,X5),X2))),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X2)) ) ),
introduced(choice_axiom,[]) ).
thf(f1425,plain,
! [X0: product_prod_nat_nat > a,X1: nat,X2: list_P559422087at_nat,X3: nat,X4: nat,X5: nat] :
( ? [X6: nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X5),X6)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X2)) )
| ( X3 = X5 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X4),X5)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X2)) )
| ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,X0),X1),X2),X3) ) ),
inference(flattening,[],[f1424]) ).
thf(f1424,plain,
! [X0: product_prod_nat_nat > a,X1: nat,X2: list_P559422087at_nat,X3: nat,X4: nat,X5: nat] :
( ? [X6: nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X5),X6)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X2)) )
| ( X3 = X5 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X4),X5)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X2)) )
| ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,X0),X1),X2),X3) ) ),
inference(ennf_transformation,[],[f1009]) ).
thf(f1009,plain,
! [X0: product_prod_nat_nat > a,X1: nat,X2: list_P559422087at_nat,X3: nat,X4: nat,X5: nat] :
( ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,X0),X1),X2),X3) )
=> ( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X4),X5)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X2)) )
=> ( ( X3 != X5 )
=> ? [X6: nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X5),X6)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X2)) ) ) ) ),
inference(fool_elimination,[],[f1008]) ).
thf(f1008,plain,
! [X0: product_prod_nat_nat > a,X1: nat,X2: list_P559422087at_nat,X3: nat,X4: nat,X5: nat] :
( vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,X0),X1),X2),X3)
=> ( vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X4),X5)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X2))
=> ( ( X3 != X5 )
=> ? [X6: nat] : vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X5),X6)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X2)) ) ) ),
inference(rectify,[],[f185]) ).
thf(f185,axiom,
! [X9: product_prod_nat_nat > a,X1: nat,X6: list_P559422087at_nat,X7: nat,X33: nat,X34: nat] :
( vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,X9),X1),X6),X7)
=> ( vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X33),X34)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X6))
=> ( ( X7 != X34 )
=> ? [X35: nat] : vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X34),X35)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X6)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_Graph_OisPath__ex__edge2) ).
thf(f3146,plain,
spl155_56,
inference(avatar_split_clause,[],[f2081,f3144]) ).
thf(f2081,plain,
! [X2: nat,X3: nat,X0: nat,X1: list_P559422087at_nat,X4: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(list_P559422087at_nat,nat,vAPP(nat,sTfun(list_P559422087at_nat,nat),sK152,X3),X1)),X3)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X1)) )
| ( X0 = X3 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X3),X4)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X1)) )
| ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2) ) ),
inference(cnf_transformation,[],[f1614]) ).
thf(f1614,plain,
! [X0: nat,X1: list_P559422087at_nat,X2: nat,X3: nat,X4: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(list_P559422087at_nat,nat,vAPP(nat,sTfun(list_P559422087at_nat,nat),sK152,X3),X1)),X3)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X1)) )
| ( X0 = X3 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X3),X4)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X1)) )
| ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK152])],[f1419,f1613]) ).
thf(f1613,plain,
! [X1: list_P559422087at_nat,X3: nat] :
( ? [X5: nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X5),X3)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X1)) )
=> ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(list_P559422087at_nat,nat,vAPP(nat,sTfun(list_P559422087at_nat,nat),sK152,X3),X1)),X3)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X1)) ) ),
introduced(choice_axiom,[]) ).
thf(f1419,plain,
! [X0: nat,X1: list_P559422087at_nat,X2: nat,X3: nat,X4: nat] :
( ? [X5: nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X5),X3)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X1)) )
| ( X0 = X3 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X3),X4)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X1)) )
| ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2) ) ),
inference(flattening,[],[f1418]) ).
thf(f1418,plain,
! [X0: nat,X1: list_P559422087at_nat,X2: nat,X3: nat,X4: nat] :
( ? [X5: nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X5),X3)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X1)) )
| ( X0 = X3 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X3),X4)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X1)) )
| ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2) ) ),
inference(ennf_transformation,[],[f1003]) ).
thf(f1003,plain,
! [X0: nat,X1: list_P559422087at_nat,X2: nat,X3: nat,X4: nat] :
( ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2) )
=> ( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X3),X4)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X1)) )
=> ( ( X0 != X3 )
=> ? [X5: nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X5),X3)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X1)) ) ) ) ),
inference(fool_elimination,[],[f1002]) ).
thf(f1002,plain,
! [X0: nat,X1: list_P559422087at_nat,X2: nat,X3: nat,X4: nat] :
( vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2)
=> ( vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X3),X4)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X1))
=> ( ( X0 != X3 )
=> ? [X5: nat] : vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X5),X3)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X1)) ) ) ),
inference(rectify,[],[f153]) ).
thf(f153,axiom,
! [X1: nat,X6: list_P559422087at_nat,X7: nat,X33: nat,X34: nat] :
( vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X1),X6),X7)
=> ( vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X33),X34)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X6))
=> ( ( X1 != X33 )
=> ? [X36: nat] : vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X36),X33)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X6)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_isPath__ex__edge1) ).
thf(f3142,plain,
spl155_55,
inference(avatar_split_clause,[],[f2080,f3140]) ).
thf(f2080,plain,
! [X2: nat,X3: nat,X0: nat,X1: list_P559422087at_nat,X4: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X4),vAPP(list_P559422087at_nat,nat,vAPP(nat,sTfun(list_P559422087at_nat,nat),sK151,X4),X1))),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X1)) )
| ( X2 = X4 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X3),X4)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X1)) )
| ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2) ) ),
inference(cnf_transformation,[],[f1612]) ).
thf(f1612,plain,
! [X0: nat,X1: list_P559422087at_nat,X2: nat,X3: nat,X4: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X4),vAPP(list_P559422087at_nat,nat,vAPP(nat,sTfun(list_P559422087at_nat,nat),sK151,X4),X1))),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X1)) )
| ( X2 = X4 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X3),X4)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X1)) )
| ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK151])],[f1417,f1611]) ).
thf(f1611,plain,
! [X1: list_P559422087at_nat,X4: nat] :
( ? [X5: nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X4),X5)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X1)) )
=> ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X4),vAPP(list_P559422087at_nat,nat,vAPP(nat,sTfun(list_P559422087at_nat,nat),sK151,X4),X1))),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X1)) ) ),
introduced(choice_axiom,[]) ).
thf(f1417,plain,
! [X0: nat,X1: list_P559422087at_nat,X2: nat,X3: nat,X4: nat] :
( ? [X5: nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X4),X5)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X1)) )
| ( X2 = X4 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X3),X4)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X1)) )
| ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2) ) ),
inference(flattening,[],[f1416]) ).
thf(f1416,plain,
! [X0: nat,X1: list_P559422087at_nat,X2: nat,X3: nat,X4: nat] :
( ? [X5: nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X4),X5)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X1)) )
| ( X2 = X4 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X3),X4)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X1)) )
| ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2) ) ),
inference(ennf_transformation,[],[f1001]) ).
thf(f1001,plain,
! [X0: nat,X1: list_P559422087at_nat,X2: nat,X3: nat,X4: nat] :
( ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2) )
=> ( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X3),X4)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X1)) )
=> ( ( X2 != X4 )
=> ? [X5: nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X4),X5)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X1)) ) ) ) ),
inference(fool_elimination,[],[f1000]) ).
thf(f1000,plain,
! [X0: nat,X1: list_P559422087at_nat,X2: nat,X3: nat,X4: nat] :
( vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2)
=> ( vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X3),X4)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X1))
=> ( ( X2 != X4 )
=> ? [X5: nat] : vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X4),X5)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X1)) ) ) ),
inference(rectify,[],[f148]) ).
thf(f148,axiom,
! [X1: nat,X6: list_P559422087at_nat,X7: nat,X33: nat,X34: nat] :
( vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X1),X6),X7)
=> ( vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X33),X34)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X6))
=> ( ( X7 != X34 )
=> ? [X35: nat] : vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X34),X35)),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X6)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_isPath__ex__edge2) ).
thf(f3136,plain,
spl155_54,
inference(avatar_split_clause,[],[f1979,f3134]) ).
thf(f1979,plain,
! [X2: list_P559422087at_nat,X0: nat,X1: nat] :
( ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,nat)),sK64,X2),X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,nat)),sK65,X2),X1),X0))),vAPP(nat,list_P559422087at_nat,vAPP(nat,sTfun(nat,list_P559422087at_nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,list_P559422087at_nat)),sK66,X2),X1),X0)) = X2 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,$o)),sP7,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f1528]) ).
thf(f1528,plain,
! [X0: nat,X1: nat,X2: list_P559422087at_nat] :
( ( ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,nat)),sK65,X2),X1),X0)),vAPP(nat,list_P559422087at_nat,vAPP(nat,sTfun(nat,list_P559422087at_nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,list_P559422087at_nat)),sK66,X2),X1),X0)),X0) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,nat)),sK64,X2),X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,nat)),sK65,X2),X1),X0))),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) )
& ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,nat)),sK64,X2),X1),X0) = X1 )
& ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,nat)),sK64,X2),X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,nat)),sK65,X2),X1),X0))),vAPP(nat,list_P559422087at_nat,vAPP(nat,sTfun(nat,list_P559422087at_nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,list_P559422087at_nat)),sK66,X2),X1),X0)) = X2 ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,$o)),sP7,X2),X1),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK64,sK65,sK66])],[f1526,f1527]) ).
thf(f1527,plain,
! [X0: nat,X1: nat,X2: list_P559422087at_nat] :
( ? [X3: nat,X4: nat,X5: list_P559422087at_nat] :
( ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X4),X5),X0) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X3),X4)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) )
& ( X1 = X3 )
& ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X3),X4)),X5) = X2 ) )
=> ( ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,nat)),sK65,X2),X1),X0)),vAPP(nat,list_P559422087at_nat,vAPP(nat,sTfun(nat,list_P559422087at_nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,list_P559422087at_nat)),sK66,X2),X1),X0)),X0) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,nat)),sK64,X2),X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,nat)),sK65,X2),X1),X0))),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) )
& ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,nat)),sK64,X2),X1),X0) = X1 )
& ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,nat)),sK64,X2),X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,nat)),sK65,X2),X1),X0))),vAPP(nat,list_P559422087at_nat,vAPP(nat,sTfun(nat,list_P559422087at_nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,list_P559422087at_nat)),sK66,X2),X1),X0)) = X2 ) ) ),
introduced(choice_axiom,[]) ).
thf(f1526,plain,
! [X0: nat,X1: nat,X2: list_P559422087at_nat] :
( ? [X3: nat,X4: nat,X5: list_P559422087at_nat] :
( ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X4),X5),X0) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X3),X4)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) )
& ( X1 = X3 )
& ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X3),X4)),X5) = X2 ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,$o)),sP7,X2),X1),X0) ) ),
inference(rectify,[],[f1525]) ).
thf(f1525,plain,
! [X2: nat,X0: nat,X1: list_P559422087at_nat] :
( ? [X3: nat,X4: nat,X5: list_P559422087at_nat] :
( ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X4),X5),X2) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X3),X4)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) )
& ( X0 = X3 )
& ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X3),X4)),X5) = X1 ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,$o)),sP7,X1),X0),X2) ) ),
inference(nnf_transformation,[],[f1439]) ).
thf(f1439,plain,
! [X2: nat,X0: nat,X1: list_P559422087at_nat] :
( ? [X3: nat,X4: nat,X5: list_P559422087at_nat] :
( ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X4),X5),X2) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X3),X4)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) )
& ( X0 = X3 )
& ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X3),X4)),X5) = X1 ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,$o)),sP7,X1),X0),X2) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f3128,plain,
spl155_53,
inference(avatar_split_clause,[],[f1982,f3126]) ).
thf(f1982,plain,
! [X2: list_P559422087at_nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,nat)),sK65,X2),X1),X0)),vAPP(nat,list_P559422087at_nat,vAPP(nat,sTfun(nat,list_P559422087at_nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,list_P559422087at_nat)),sK66,X2),X1),X0)),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,$o)),sP7,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f1528]) ).
thf(f3124,plain,
spl155_52,
inference(avatar_split_clause,[],[f1976,f3122]) ).
thf(f1976,plain,
! [X2: list_P559422087at_nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,nat)),sK63,X2),X1),X0)),vAPP(nat,list_P559422087at_nat,vAPP(nat,sTfun(nat,list_P559422087at_nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,list_P559422087at_nat)),sK62,X2),X1),X0)),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,$o)),sP6,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f1524]) ).
thf(f1524,plain,
! [X0: nat,X1: nat,X2: list_P559422087at_nat] :
( ( ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,nat)),sK63,X2),X1),X0)),vAPP(nat,list_P559422087at_nat,vAPP(nat,sTfun(nat,list_P559422087at_nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,list_P559422087at_nat)),sK62,X2),X1),X0)),X0) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,nat)),sK63,X2),X1),X0))),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) )
& ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,nat)),sK63,X2),X1),X0))),vAPP(nat,list_P559422087at_nat,vAPP(nat,sTfun(nat,list_P559422087at_nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,list_P559422087at_nat)),sK62,X2),X1),X0)) = X2 ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,$o)),sP6,X2),X1),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK62,sK63])],[f1522,f1523]) ).
thf(f1523,plain,
! [X0: nat,X1: nat,X2: list_P559422087at_nat] :
( ? [X3: list_P559422087at_nat,X4: nat] :
( ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X4),X3),X0) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X1),X4)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) )
& ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X1),X4)),X3) = X2 ) )
=> ( ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,nat)),sK63,X2),X1),X0)),vAPP(nat,list_P559422087at_nat,vAPP(nat,sTfun(nat,list_P559422087at_nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,list_P559422087at_nat)),sK62,X2),X1),X0)),X0) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,nat)),sK63,X2),X1),X0))),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) )
& ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,nat)),sK63,X2),X1),X0))),vAPP(nat,list_P559422087at_nat,vAPP(nat,sTfun(nat,list_P559422087at_nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,list_P559422087at_nat)),sK62,X2),X1),X0)) = X2 ) ) ),
introduced(choice_axiom,[]) ).
thf(f1522,plain,
! [X0: nat,X1: nat,X2: list_P559422087at_nat] :
( ? [X3: list_P559422087at_nat,X4: nat] :
( ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X4),X3),X0) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X1),X4)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) )
& ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X1),X4)),X3) = X2 ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,$o)),sP6,X2),X1),X0) ) ),
inference(rectify,[],[f1521]) ).
thf(f1521,plain,
! [X2: nat,X0: nat,X1: list_P559422087at_nat] :
( ? [X3: list_P559422087at_nat,X4: nat] :
( ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X4),X3),X2) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X0),X4)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) )
& ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X0),X4)),X3) = X1 ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,$o)),sP6,X1),X0),X2) ) ),
inference(nnf_transformation,[],[f1437]) ).
thf(f1437,plain,
! [X2: nat,X0: nat,X1: list_P559422087at_nat] :
( ? [X3: list_P559422087at_nat,X4: nat] :
( ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X4),X3),X2) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X0),X4)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) )
& ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X0),X4)),X3) = X1 ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,$o)),sP6,X1),X0),X2) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f3120,plain,
( spl155_51
| ~ spl155_5
| ~ spl155_6 ),
inference(avatar_split_clause,[],[f2793,f2785,f2780,f3117]) ).
thf(f3117,plain,
( spl155_51
<=> ( vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c) = vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,vAPP(set_Pr1986765409at_nat,list_P559422087at_nat,sK9,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_51])]) ).
thf(f2793,plain,
( ( vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c) = vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,vAPP(set_Pr1986765409at_nat,list_P559422087at_nat,sK9,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c))) )
| ~ spl155_5
| ~ spl155_6 ),
inference(trivial_inequality_removal,[],[f2790]) ).
thf(f2790,plain,
( ( $true != $true )
| ( vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c) = vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,vAPP(set_Pr1986765409at_nat,list_P559422087at_nat,sK9,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c))) )
| ~ spl155_5
| ~ spl155_6 ),
inference(superposition,[],[f2786,f2782]) ).
thf(f3113,plain,
spl155_50,
inference(avatar_split_clause,[],[f1981,f3111]) ).
thf(f1981,plain,
! [X2: list_P559422087at_nat,X0: nat,X1: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,nat)),sK64,X2),X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,nat)),sK65,X2),X1),X0))),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,$o)),sP7,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f1528]) ).
thf(f3107,plain,
spl155_49,
inference(avatar_split_clause,[],[f1974,f3105]) ).
thf(f1974,plain,
! [X2: list_P559422087at_nat,X0: nat,X1: nat] :
( ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,nat)),sK63,X2),X1),X0))),vAPP(nat,list_P559422087at_nat,vAPP(nat,sTfun(nat,list_P559422087at_nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,list_P559422087at_nat)),sK62,X2),X1),X0)) = X2 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,$o)),sP6,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f1524]) ).
thf(f3101,plain,
spl155_48,
inference(avatar_split_clause,[],[f2075,f3099]) ).
thf(f2075,plain,
! [X2: nat,X3: nat,X0: nat,X1: product_prod_nat_nat > a] :
( ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X3),vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),reachableNodes_a,X1),X2)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X0),X3)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X1)) )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),reachableNodes_a,X1),X2)) ) ),
inference(cnf_transformation,[],[f1410]) ).
thf(f1410,plain,
! [X0: nat,X1: product_prod_nat_nat > a,X2: nat,X3: nat] :
( ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X3),vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),reachableNodes_a,X1),X2)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X0),X3)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X1)) )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),reachableNodes_a,X1),X2)) ) ),
inference(flattening,[],[f1409]) ).
thf(f1409,plain,
! [X0: nat,X1: product_prod_nat_nat > a,X2: nat,X3: nat] :
( ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X3),vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),reachableNodes_a,X1),X2)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X0),X3)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X1)) )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),reachableNodes_a,X1),X2)) ) ),
inference(ennf_transformation,[],[f991]) ).
thf(f991,plain,
! [X0: nat,X1: product_prod_nat_nat > a,X2: nat,X3: nat] :
( ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),reachableNodes_a,X1),X2)) )
=> ( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X0),X3)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X1)) )
=> ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X3),vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),reachableNodes_a,X1),X2)) ) ) ),
inference(fool_elimination,[],[f990]) ).
thf(f990,plain,
! [X0: nat,X1: product_prod_nat_nat > a,X2: nat,X3: nat] :
( vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),reachableNodes_a,X1),X2))
=> ( vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X0),X3)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X1))
=> vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X3),vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),reachableNodes_a,X1),X2)) ) ),
inference(rectify,[],[f166]) ).
thf(f166,axiom,
! [X1: nat,X9: product_prod_nat_nat > a,X10: nat,X7: nat] :
( vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X1),vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),reachableNodes_a,X9),X10))
=> ( vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X1),X7)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X9))
=> vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X7),vAPP(nat,set_nat,vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,set_nat),reachableNodes_a,X9),X10)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_Graph_OreachableNodes__append__edge) ).
thf(f3091,plain,
spl155_47,
inference(avatar_split_clause,[],[f1827,f3089]) ).
thf(f1827,plain,
! [X0: product_prod_nat_nat,X1: list_P559422087at_nat] :
( ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(product_prod_nat_nat,product_prod_nat_nat,vAPP(list_P559422087at_nat,sTfun(product_prod_nat_nat,product_prod_nat_nat),sK29,X1),X0)),vAPP(product_prod_nat_nat,list_P559422087at_nat,vAPP(list_P559422087at_nat,sTfun(product_prod_nat_nat,list_P559422087at_nat),sK30,X1),X0)) = X1 )
| ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,X0),vAPP(product_prod_nat_nat,list_P559422087at_nat,vAPP(list_P559422087at_nat,sTfun(product_prod_nat_nat,list_P559422087at_nat),sK31,X1),X0)) = X1 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X1)) ) ),
inference(cnf_transformation,[],[f1488]) ).
thf(f1488,plain,
! [X0: product_prod_nat_nat,X1: list_P559422087at_nat] :
( ( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,vAPP(product_prod_nat_nat,list_P559422087at_nat,vAPP(list_P559422087at_nat,sTfun(product_prod_nat_nat,list_P559422087at_nat),sK30,X1),X0))) )
& ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(product_prod_nat_nat,product_prod_nat_nat,vAPP(list_P559422087at_nat,sTfun(product_prod_nat_nat,product_prod_nat_nat),sK29,X1),X0)),vAPP(product_prod_nat_nat,list_P559422087at_nat,vAPP(list_P559422087at_nat,sTfun(product_prod_nat_nat,list_P559422087at_nat),sK30,X1),X0)) = X1 ) )
| ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,X0),vAPP(product_prod_nat_nat,list_P559422087at_nat,vAPP(list_P559422087at_nat,sTfun(product_prod_nat_nat,list_P559422087at_nat),sK31,X1),X0)) = X1 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK29,sK30,sK31])],[f1485,f1487,f1486]) ).
thf(f1486,plain,
! [X0: product_prod_nat_nat,X1: list_P559422087at_nat] :
( ? [X2: product_prod_nat_nat,X3: list_P559422087at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X3)) )
& ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,X2),X3) = X1 ) )
=> ( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,vAPP(product_prod_nat_nat,list_P559422087at_nat,vAPP(list_P559422087at_nat,sTfun(product_prod_nat_nat,list_P559422087at_nat),sK30,X1),X0))) )
& ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(product_prod_nat_nat,product_prod_nat_nat,vAPP(list_P559422087at_nat,sTfun(product_prod_nat_nat,product_prod_nat_nat),sK29,X1),X0)),vAPP(product_prod_nat_nat,list_P559422087at_nat,vAPP(list_P559422087at_nat,sTfun(product_prod_nat_nat,list_P559422087at_nat),sK30,X1),X0)) = X1 ) ) ),
introduced(choice_axiom,[]) ).
thf(f1487,plain,
! [X0: product_prod_nat_nat,X1: list_P559422087at_nat] :
( ? [X4: list_P559422087at_nat] : ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,X0),X4) = X1 )
=> ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,X0),vAPP(product_prod_nat_nat,list_P559422087at_nat,vAPP(list_P559422087at_nat,sTfun(product_prod_nat_nat,list_P559422087at_nat),sK31,X1),X0)) = X1 ) ),
introduced(choice_axiom,[]) ).
thf(f1485,plain,
! [X0: product_prod_nat_nat,X1: list_P559422087at_nat] :
( ? [X2: product_prod_nat_nat,X3: list_P559422087at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X3)) )
& ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,X2),X3) = X1 ) )
| ? [X4: list_P559422087at_nat] : ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,X0),X4) = X1 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X1)) ) ),
inference(rectify,[],[f1198]) ).
thf(f1198,plain,
! [X0: product_prod_nat_nat,X1: list_P559422087at_nat] :
( ? [X3: product_prod_nat_nat,X4: list_P559422087at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X4)) )
& ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,X3),X4) = X1 ) )
| ? [X2: list_P559422087at_nat] : ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,X0),X2) = X1 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X1)) ) ),
inference(flattening,[],[f1197]) ).
thf(f1197,plain,
! [X0: product_prod_nat_nat,X1: list_P559422087at_nat] :
( ? [X3: product_prod_nat_nat,X4: list_P559422087at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X4)) )
& ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,X3),X4) = X1 ) )
| ? [X2: list_P559422087at_nat] : ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,X0),X2) = X1 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X1)) ) ),
inference(ennf_transformation,[],[f1049]) ).
thf(f1049,plain,
! [X0: product_prod_nat_nat,X1: list_P559422087at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X1)) )
=> ( ! [X2: list_P559422087at_nat] : ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,X0),X2) != X1 )
=> ~ ! [X3: product_prod_nat_nat,X4: list_P559422087at_nat] :
( ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,X3),X4) = X1 )
=> ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X4)) ) ) ) ),
inference(flattening,[],[f671]) ).
thf(f671,plain,
! [X0: product_prod_nat_nat,X1: list_P559422087at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X1)) )
=> ( ! [X2: list_P559422087at_nat] : ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,X0),X2) != X1 )
=> ~ ! [X3: product_prod_nat_nat,X4: list_P559422087at_nat] :
( ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,X3),X4) = X1 )
=> ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X4)) ) ) ) ),
inference(fool_elimination,[],[f670]) ).
thf(f670,plain,
! [X0: product_prod_nat_nat,X1: list_P559422087at_nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X1))
=> ( ! [X2: list_P559422087at_nat] : ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,X0),X2) != X1 )
=> ~ ! [X3: product_prod_nat_nat,X4: list_P559422087at_nat] :
( ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,X3),X4) = X1 )
=> ~ vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X4)) ) ) ),
inference(rectify,[],[f345]) ).
thf(f345,axiom,
! [X8: product_prod_nat_nat,X13: list_P559422087at_nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X8),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X13))
=> ( ! [X58: list_P559422087at_nat] : ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,X8),X58) != X13 )
=> ~ ! [X59: product_prod_nat_nat,X58: list_P559422087at_nat] :
( ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,X59),X58) = X13 )
=> ~ vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X8),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X58)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_344_list_Oset__cases) ).
thf(f3087,plain,
spl155_46,
inference(avatar_split_clause,[],[f1819,f3085]) ).
thf(f1819,plain,
! [X0: nat,X1: list_nat] :
( ( vAPP(list_nat,list_nat,vAPP(nat,sTfun(list_nat,list_nat),cons_nat,vAPP(nat,nat,vAPP(list_nat,sTfun(nat,nat),sK24,X1),X0)),vAPP(nat,list_nat,vAPP(list_nat,sTfun(nat,list_nat),sK25,X1),X0)) = X1 )
| ( vAPP(list_nat,list_nat,vAPP(nat,sTfun(list_nat,list_nat),cons_nat,X0),vAPP(nat,list_nat,vAPP(list_nat,sTfun(nat,list_nat),sK26,X1),X0)) = X1 )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(list_nat,set_nat,set_nat2,X1)) ) ),
inference(cnf_transformation,[],[f1480]) ).
thf(f1480,plain,
! [X0: nat,X1: list_nat] :
( ( ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(list_nat,set_nat,set_nat2,vAPP(nat,list_nat,vAPP(list_nat,sTfun(nat,list_nat),sK25,X1),X0))) )
& ( vAPP(list_nat,list_nat,vAPP(nat,sTfun(list_nat,list_nat),cons_nat,vAPP(nat,nat,vAPP(list_nat,sTfun(nat,nat),sK24,X1),X0)),vAPP(nat,list_nat,vAPP(list_nat,sTfun(nat,list_nat),sK25,X1),X0)) = X1 ) )
| ( vAPP(list_nat,list_nat,vAPP(nat,sTfun(list_nat,list_nat),cons_nat,X0),vAPP(nat,list_nat,vAPP(list_nat,sTfun(nat,list_nat),sK26,X1),X0)) = X1 )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(list_nat,set_nat,set_nat2,X1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK24,sK25,sK26])],[f1477,f1479,f1478]) ).
thf(f1478,plain,
! [X0: nat,X1: list_nat] :
( ? [X2: nat,X3: list_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(list_nat,set_nat,set_nat2,X3)) )
& ( vAPP(list_nat,list_nat,vAPP(nat,sTfun(list_nat,list_nat),cons_nat,X2),X3) = X1 ) )
=> ( ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(list_nat,set_nat,set_nat2,vAPP(nat,list_nat,vAPP(list_nat,sTfun(nat,list_nat),sK25,X1),X0))) )
& ( vAPP(list_nat,list_nat,vAPP(nat,sTfun(list_nat,list_nat),cons_nat,vAPP(nat,nat,vAPP(list_nat,sTfun(nat,nat),sK24,X1),X0)),vAPP(nat,list_nat,vAPP(list_nat,sTfun(nat,list_nat),sK25,X1),X0)) = X1 ) ) ),
introduced(choice_axiom,[]) ).
thf(f1479,plain,
! [X0: nat,X1: list_nat] :
( ? [X4: list_nat] : ( vAPP(list_nat,list_nat,vAPP(nat,sTfun(list_nat,list_nat),cons_nat,X0),X4) = X1 )
=> ( vAPP(list_nat,list_nat,vAPP(nat,sTfun(list_nat,list_nat),cons_nat,X0),vAPP(nat,list_nat,vAPP(list_nat,sTfun(nat,list_nat),sK26,X1),X0)) = X1 ) ),
introduced(choice_axiom,[]) ).
thf(f1477,plain,
! [X0: nat,X1: list_nat] :
( ? [X2: nat,X3: list_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(list_nat,set_nat,set_nat2,X3)) )
& ( vAPP(list_nat,list_nat,vAPP(nat,sTfun(list_nat,list_nat),cons_nat,X2),X3) = X1 ) )
| ? [X4: list_nat] : ( vAPP(list_nat,list_nat,vAPP(nat,sTfun(list_nat,list_nat),cons_nat,X0),X4) = X1 )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(list_nat,set_nat,set_nat2,X1)) ) ),
inference(rectify,[],[f1192]) ).
thf(f1192,plain,
! [X0: nat,X1: list_nat] :
( ? [X3: nat,X4: list_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(list_nat,set_nat,set_nat2,X4)) )
& ( vAPP(list_nat,list_nat,vAPP(nat,sTfun(list_nat,list_nat),cons_nat,X3),X4) = X1 ) )
| ? [X2: list_nat] : ( vAPP(list_nat,list_nat,vAPP(nat,sTfun(list_nat,list_nat),cons_nat,X0),X2) = X1 )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(list_nat,set_nat,set_nat2,X1)) ) ),
inference(flattening,[],[f1191]) ).
thf(f1191,plain,
! [X0: nat,X1: list_nat] :
( ? [X3: nat,X4: list_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(list_nat,set_nat,set_nat2,X4)) )
& ( vAPP(list_nat,list_nat,vAPP(nat,sTfun(list_nat,list_nat),cons_nat,X3),X4) = X1 ) )
| ? [X2: list_nat] : ( vAPP(list_nat,list_nat,vAPP(nat,sTfun(list_nat,list_nat),cons_nat,X0),X2) = X1 )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(list_nat,set_nat,set_nat2,X1)) ) ),
inference(ennf_transformation,[],[f1046]) ).
thf(f1046,plain,
! [X0: nat,X1: list_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(list_nat,set_nat,set_nat2,X1)) )
=> ( ! [X2: list_nat] : ( vAPP(list_nat,list_nat,vAPP(nat,sTfun(list_nat,list_nat),cons_nat,X0),X2) != X1 )
=> ~ ! [X3: nat,X4: list_nat] :
( ( vAPP(list_nat,list_nat,vAPP(nat,sTfun(list_nat,list_nat),cons_nat,X3),X4) = X1 )
=> ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(list_nat,set_nat,set_nat2,X4)) ) ) ) ),
inference(flattening,[],[f665]) ).
thf(f665,plain,
! [X0: nat,X1: list_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(list_nat,set_nat,set_nat2,X1)) )
=> ( ! [X2: list_nat] : ( vAPP(list_nat,list_nat,vAPP(nat,sTfun(list_nat,list_nat),cons_nat,X0),X2) != X1 )
=> ~ ! [X3: nat,X4: list_nat] :
( ( vAPP(list_nat,list_nat,vAPP(nat,sTfun(list_nat,list_nat),cons_nat,X3),X4) = X1 )
=> ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(list_nat,set_nat,set_nat2,X4)) ) ) ) ),
inference(fool_elimination,[],[f664]) ).
thf(f664,plain,
! [X0: nat,X1: list_nat] :
( vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(list_nat,set_nat,set_nat2,X1))
=> ( ! [X2: list_nat] : ( vAPP(list_nat,list_nat,vAPP(nat,sTfun(list_nat,list_nat),cons_nat,X0),X2) != X1 )
=> ~ ! [X3: nat,X4: list_nat] :
( ( vAPP(list_nat,list_nat,vAPP(nat,sTfun(list_nat,list_nat),cons_nat,X3),X4) = X1 )
=> ~ vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(list_nat,set_nat,set_nat2,X4)) ) ) ),
inference(rectify,[],[f344]) ).
thf(f344,axiom,
! [X8: nat,X13: list_nat] :
( vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X8),vAPP(list_nat,set_nat,set_nat2,X13))
=> ( ! [X58: list_nat] : ( vAPP(list_nat,list_nat,vAPP(nat,sTfun(list_nat,list_nat),cons_nat,X8),X58) != X13 )
=> ~ ! [X59: nat,X58: list_nat] :
( ( vAPP(list_nat,list_nat,vAPP(nat,sTfun(list_nat,list_nat),cons_nat,X59),X58) = X13 )
=> ~ vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X8),vAPP(list_nat,set_nat,set_nat2,X58)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_343_list_Oset__cases) ).
thf(f3063,plain,
spl155_45,
inference(avatar_split_clause,[],[f1890,f3061]) ).
thf(f1890,plain,
! [X2: nat,X0: nat > nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK36,X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK37,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK38,X0)) ) ),
inference(cnf_transformation,[],[f1501]) ).
thf(f3059,plain,
spl155_44,
inference(avatar_split_clause,[],[f1888,f3057]) ).
thf(f1888,plain,
! [X2: nat,X0: nat > nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK36,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK37,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK38,X0)) ) ),
inference(cnf_transformation,[],[f1501]) ).
thf(f3053,plain,
spl155_43,
inference(avatar_split_clause,[],[f2082,f3051]) ).
thf(f2082,plain,
! [X2: list_P559422087at_nat,X3: nat,X0: product_prod_nat_nat > a,X1: nat,X4: product_prod_nat_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X4),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X4),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X2)) )
| ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,X0),X1),X2),X3) ) ),
inference(cnf_transformation,[],[f1421]) ).
thf(f1421,plain,
! [X0: product_prod_nat_nat > a,X1: nat,X2: list_P559422087at_nat,X3: nat,X4: product_prod_nat_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X4),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X4),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X2)) )
| ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,X0),X1),X2),X3) ) ),
inference(flattening,[],[f1420]) ).
thf(f1420,plain,
! [X0: product_prod_nat_nat > a,X1: nat,X2: list_P559422087at_nat,X3: nat,X4: product_prod_nat_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X4),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X4),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X2)) )
| ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,X0),X1),X2),X3) ) ),
inference(ennf_transformation,[],[f1005]) ).
thf(f1005,plain,
! [X0: product_prod_nat_nat > a,X1: nat,X2: list_P559422087at_nat,X3: nat,X4: product_prod_nat_nat] :
( ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,X0),X1),X2),X3) )
=> ( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X4),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X2)) )
=> ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X4),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) ) ) ),
inference(fool_elimination,[],[f1004]) ).
thf(f1004,plain,
! [X0: product_prod_nat_nat > a,X1: nat,X2: list_P559422087at_nat,X3: nat,X4: product_prod_nat_nat] :
( vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,X0),X1),X2),X3)
=> ( vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X4),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X2))
=> vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X4),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X0)) ) ),
inference(rectify,[],[f147]) ).
thf(f147,axiom,
! [X9: product_prod_nat_nat > a,X1: nat,X6: list_P559422087at_nat,X7: nat,X8: product_prod_nat_nat] :
( vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,X9),X1),X6),X7)
=> ( vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X8),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X6))
=> vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X8),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,X9)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_Graph_OisPath__edgeset) ).
thf(f3047,plain,
spl155_42,
inference(avatar_split_clause,[],[f1975,f3045]) ).
thf(f1975,plain,
! [X2: list_P559422087at_nat,X0: nat,X1: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,nat)),sK63,X2),X1),X0))),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,$o)),sP6,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f1524]) ).
thf(f3029,plain,
spl155_41,
inference(avatar_split_clause,[],[f1828,f3027]) ).
thf(f1828,plain,
! [X0: product_prod_nat_nat,X1: list_P559422087at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,vAPP(product_prod_nat_nat,list_P559422087at_nat,vAPP(list_P559422087at_nat,sTfun(product_prod_nat_nat,list_P559422087at_nat),sK30,X1),X0))) )
| ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,X0),vAPP(product_prod_nat_nat,list_P559422087at_nat,vAPP(list_P559422087at_nat,sTfun(product_prod_nat_nat,list_P559422087at_nat),sK31,X1),X0)) = X1 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X1)) ) ),
inference(cnf_transformation,[],[f1488]) ).
thf(f3025,plain,
spl155_40,
inference(avatar_split_clause,[],[f1820,f3023]) ).
thf(f1820,plain,
! [X0: nat,X1: list_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(list_nat,set_nat,set_nat2,vAPP(nat,list_nat,vAPP(list_nat,sTfun(nat,list_nat),sK25,X1),X0))) )
| ( vAPP(list_nat,list_nat,vAPP(nat,sTfun(list_nat,list_nat),cons_nat,X0),vAPP(nat,list_nat,vAPP(list_nat,sTfun(nat,list_nat),sK26,X1),X0)) = X1 )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(list_nat,set_nat,set_nat2,X1)) ) ),
inference(cnf_transformation,[],[f1480]) ).
thf(f3017,plain,
spl155_39,
inference(avatar_split_clause,[],[f2077,f3015]) ).
thf(f2077,plain,
! [X2: list_P559422087at_nat,X3: nat,X0: product_prod_nat_nat > a,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,X0),X1),X2),X3) )
| ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isShortestPath_a,X0),X1),X2),X3) ) ),
inference(cnf_transformation,[],[f1413]) ).
thf(f1413,plain,
! [X0: product_prod_nat_nat > a,X1: nat,X2: list_P559422087at_nat,X3: nat] :
( ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,X0),X1),X2),X3) )
| ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isShortestPath_a,X0),X1),X2),X3) ) ),
inference(ennf_transformation,[],[f995]) ).
thf(f995,plain,
! [X0: product_prod_nat_nat > a,X1: nat,X2: list_P559422087at_nat,X3: nat] :
( ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isShortestPath_a,X0),X1),X2),X3) )
=> ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,X0),X1),X2),X3) ) ),
inference(fool_elimination,[],[f994]) ).
thf(f994,plain,
! [X0: product_prod_nat_nat > a,X1: nat,X2: list_P559422087at_nat,X3: nat] :
( vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isShortestPath_a,X0),X1),X2),X3)
=> vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,X0),X1),X2),X3) ),
inference(rectify,[],[f201]) ).
thf(f201,axiom,
! [X9: product_prod_nat_nat > a,X1: nat,X6: list_P559422087at_nat,X7: nat] :
( vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isShortestPath_a,X9),X1),X6),X7)
=> vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,X9),X1),X6),X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_Graph_OshortestPath__is__path) ).
thf(f3005,plain,
spl155_38,
inference(avatar_split_clause,[],[f1984,f3003]) ).
thf(f1984,plain,
! [X2: nat,X0: nat,X1: list_P559422087at_nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,$o)),sP7,X1),X0),X2) )
| ( X0 = X2 )
| ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2) ) ),
inference(cnf_transformation,[],[f1440]) ).
thf(f1440,plain,
! [X0: nat,X1: list_P559422087at_nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,$o)),sP7,X1),X0),X2) )
| ( ( X0 = X2 )
& ( nil_Pr1308055047at_nat = X1 ) )
| ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2) ) ),
inference(definition_folding,[],[f1318,f1439]) ).
thf(f1318,plain,
! [X0: nat,X1: list_P559422087at_nat,X2: nat] :
( ? [X3: nat,X4: nat,X5: list_P559422087at_nat] :
( ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X4),X5),X2) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X3),X4)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) )
& ( X0 = X3 )
& ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X3),X4)),X5) = X1 ) )
| ( ( X0 = X2 )
& ( nil_Pr1308055047at_nat = X1 ) )
| ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2) ) ),
inference(flattening,[],[f1317]) ).
thf(f1317,plain,
! [X0: nat,X1: list_P559422087at_nat,X2: nat] :
( ? [X3: nat,X4: nat,X5: list_P559422087at_nat] :
( ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X4),X5),X2) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X3),X4)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) )
& ( X0 = X3 )
& ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X3),X4)),X5) = X1 ) )
| ( ( X0 = X2 )
& ( nil_Pr1308055047at_nat = X1 ) )
| ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2) ) ),
inference(ennf_transformation,[],[f897]) ).
thf(f897,plain,
! [X0: nat,X1: list_P559422087at_nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2) )
=> ( ( ( nil_Pr1308055047at_nat = X1 )
=> ( X0 != X2 ) )
=> ~ ! [X3: nat,X4: nat,X5: list_P559422087at_nat] :
( ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X3),X4)),X5) = X1 )
=> ~ ( ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X4),X5),X2) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X3),X4)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) )
& ( X0 = X3 ) ) ) ) ),
inference(fool_elimination,[],[f896]) ).
thf(f896,plain,
! [X0: nat,X1: list_P559422087at_nat,X2: nat] :
( vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2)
=> ( ( ( nil_Pr1308055047at_nat = X1 )
=> ( X0 != X2 ) )
=> ~ ! [X3: nat,X4: nat,X5: list_P559422087at_nat] :
( ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X3),X4)),X5) = X1 )
=> ~ ( vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X4),X5),X2)
& vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X3),X4)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c))
& ( X0 = X3 ) ) ) ) ),
inference(rectify,[],[f349]) ).
thf(f349,axiom,
! [X5: nat,X65: list_P559422087at_nat,X66: nat] :
( vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X5),X65),X66)
=> ( ( ( nil_Pr1308055047at_nat = X65 )
=> ( X5 != X66 ) )
=> ~ ! [X4: nat,X26: nat,X67: list_P559422087at_nat] :
( ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X4),X26)),X67) = X65 )
=> ~ ( vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X26),X67),X66)
& vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X4),X26)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c))
& ( X4 = X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_348_isPath_Oelims_I2_J) ).
thf(f3001,plain,
spl155_37,
inference(avatar_split_clause,[],[f1983,f2999]) ).
thf(f1983,plain,
! [X2: nat,X0: nat,X1: list_P559422087at_nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,$o)),sP7,X1),X0),X2) )
| ( nil_Pr1308055047at_nat = X1 )
| ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2) ) ),
inference(cnf_transformation,[],[f1440]) ).
thf(f2997,plain,
( spl155_36
| ~ spl155_3
| ~ spl155_11 ),
inference(avatar_split_clause,[],[f2840,f2814,f2771,f2995]) ).
thf(f2995,plain,
( spl155_36
<=> ! [X0: list_P559422087at_nat,X1: set_Pr1986765409at_nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_36])]) ).
thf(f2840,plain,
( ! [X0: list_P559422087at_nat,X1: set_Pr1986765409at_nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X0))) )
| ~ spl155_3
| ~ spl155_11 ),
inference(trivial_inequality_removal,[],[f2833]) ).
thf(f2833,plain,
( ! [X0: list_P559422087at_nat,X1: set_Pr1986765409at_nat] :
( ( $true != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X0))) ) )
| ~ spl155_3
| ~ spl155_11 ),
inference(superposition,[],[f2815,f2772]) ).
thf(f2993,plain,
spl155_35,
inference(avatar_split_clause,[],[f1978,f2991]) ).
thf(f1978,plain,
! [X2: nat,X0: nat,X1: list_P559422087at_nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,$o)),sP6,X1),X0),X2) )
| ( X0 = X2 )
| ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2) ) ),
inference(cnf_transformation,[],[f1438]) ).
thf(f1438,plain,
! [X0: nat,X1: list_P559422087at_nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,$o)),sP6,X1),X0),X2) )
| ( ( X0 = X2 )
& ( nil_Pr1308055047at_nat = X1 ) )
| ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2) ) ),
inference(definition_folding,[],[f1316,f1437]) ).
thf(f1316,plain,
! [X0: nat,X1: list_P559422087at_nat,X2: nat] :
( ? [X3: list_P559422087at_nat,X4: nat] :
( ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X4),X3),X2) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X0),X4)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) )
& ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X0),X4)),X3) = X1 ) )
| ( ( X0 = X2 )
& ( nil_Pr1308055047at_nat = X1 ) )
| ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2) ) ),
inference(flattening,[],[f1315]) ).
thf(f1315,plain,
! [X0: nat,X1: list_P559422087at_nat,X2: nat] :
( ? [X3: list_P559422087at_nat,X4: nat] :
( ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X4),X3),X2) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X0),X4)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) )
& ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X0),X4)),X3) = X1 ) )
| ( ( X0 = X2 )
& ( nil_Pr1308055047at_nat = X1 ) )
| ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2) ) ),
inference(ennf_transformation,[],[f1060]) ).
thf(f1060,plain,
! [X0: nat,X1: list_P559422087at_nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2) )
=> ( ( ( nil_Pr1308055047at_nat = X1 )
=> ( X0 != X2 ) )
=> ~ ! [X3: list_P559422087at_nat,X4: nat] :
( ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X0),X4)),X3) = X1 )
=> ( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X0),X4)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) )
=> ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X4),X3),X2) ) ) ) ) ),
inference(flattening,[],[f895]) ).
thf(f895,plain,
! [X0: nat,X1: list_P559422087at_nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2) )
=> ( ( ( nil_Pr1308055047at_nat = X1 )
=> ( X0 != X2 ) )
=> ~ ! [X3: list_P559422087at_nat,X4: nat] :
( ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X0),X4)),X3) = X1 )
=> ( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X0),X4)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) )
=> ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X4),X3),X2) ) ) ) ) ),
inference(fool_elimination,[],[f894]) ).
thf(f894,plain,
! [X0: nat,X1: list_P559422087at_nat,X2: nat] :
( vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2)
=> ( ( ( nil_Pr1308055047at_nat = X1 )
=> ( X0 != X2 ) )
=> ~ ! [X3: list_P559422087at_nat,X4: nat] :
( ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X0),X4)),X3) = X1 )
=> ( vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X0),X4)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c))
=> ~ vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X4),X3),X2) ) ) ) ),
inference(rectify,[],[f351]) ).
thf(f351,axiom,
! [X10: nat,X6: list_P559422087at_nat,X11: nat] :
( vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X10),X6),X11)
=> ( ( ( nil_Pr1308055047at_nat = X6 )
=> ( X10 != X11 ) )
=> ~ ! [X68: list_P559422087at_nat,X69: nat] :
( ( vAPP(list_P559422087at_nat,list_P559422087at_nat,vAPP(product_prod_nat_nat,sTfun(list_P559422087at_nat,list_P559422087at_nat),cons_P66992567at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X10),X69)),X68) = X6 )
=> ( vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X10),X69)),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c))
=> ~ vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X69),X68),X11) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_350_isPath__fwd__cases) ).
thf(f2989,plain,
spl155_34,
inference(avatar_split_clause,[],[f1977,f2987]) ).
thf(f1977,plain,
! [X2: nat,X0: nat,X1: list_P559422087at_nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,$o)),sP6,X1),X0),X2) )
| ( nil_Pr1308055047at_nat = X1 )
| ( $true != vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isPath_a,c),X0),X1),X2) ) ),
inference(cnf_transformation,[],[f1438]) ).
thf(f2979,plain,
spl155_33,
inference(avatar_split_clause,[],[f1934,f2977]) ).
thf(f1934,plain,
! [X2: set_Pr1986765409at_nat,X0: product_prod_nat_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),X2)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),X2) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1270]) ).
thf(f1270,plain,
! [X0: product_prod_nat_nat,X1: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),X2)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),X2) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),X1) ) ),
inference(flattening,[],[f1269]) ).
thf(f1269,plain,
! [X0: product_prod_nat_nat,X1: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),X2)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),X2) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),X1) ) ),
inference(ennf_transformation,[],[f831]) ).
thf(f831,plain,
! [X0: product_prod_nat_nat,X1: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),X1) )
=> ( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),X2) )
=> ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),X2)) ) ) ),
inference(fool_elimination,[],[f830]) ).
thf(f830,plain,
! [X0: product_prod_nat_nat,X1: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),X1)
=> ( vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),X2)
=> vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),X2)) ) ),
inference(rectify,[],[f150]) ).
thf(f150,axiom,
! [X9: product_prod_nat_nat,X2: set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X9),X2)
=> ( vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X9),X3)
=> vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X9),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X2),X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_IntI) ).
thf(f2975,plain,
spl155_32,
inference(avatar_split_clause,[],[f1922,f2973]) ).
thf(f1922,plain,
! [X2: set_nat,X0: nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),X2)) )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),X2) )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),X1) ) ),
inference(cnf_transformation,[],[f1250]) ).
thf(f1250,plain,
! [X0: nat,X1: set_nat,X2: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),X2)) )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),X2) )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),X1) ) ),
inference(flattening,[],[f1249]) ).
thf(f1249,plain,
! [X0: nat,X1: set_nat,X2: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),X2)) )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),X2) )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),X1) ) ),
inference(ennf_transformation,[],[f807]) ).
thf(f807,plain,
! [X0: nat,X1: set_nat,X2: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),X1) )
=> ( ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),X2) )
=> ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),X2)) ) ) ),
inference(fool_elimination,[],[f806]) ).
thf(f806,plain,
! [X0: nat,X1: set_nat,X2: set_nat] :
( vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),X1)
=> ( vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),X2)
=> vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),X2)) ) ),
inference(rectify,[],[f149]) ).
thf(f149,axiom,
! [X9: nat,X2: set_nat,X3: set_nat] :
( vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X9),X2)
=> ( vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X9),X3)
=> vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X9),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X2),X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_IntI) ).
thf(f2969,plain,
~ spl155_31,
inference(avatar_split_clause,[],[f2101,f2966]) ).
thf(f2101,plain,
$true != vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),vAPP(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),vAPP(sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),sTfun(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat)),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)))),bCOMB,vAPP(sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sTfun(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o))),bCOMB,vEQ(set_Pr1986765409at_nat))),inf_in586391887at_nat))),iCOMB),edges),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),
inference(definition_unfolding,[],[f1619,f1656]) ).
thf(f1619,plain,
vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,edges),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) != $true,
inference(cnf_transformation,[],[f1036]) ).
thf(f1036,plain,
vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,edges),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) != $true,
inference(flattening,[],[f359]) ).
thf(f359,plain,
vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,edges),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) != $true,
inference(fool_elimination,[],[f358]) ).
thf(f358,plain,
~ vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,edges),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),
inference(rectify,[],[f355]) ).
thf(f355,negated_conjecture,
~ vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,edges),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),
inference(negated_conjecture,[],[f354]) ).
thf(f354,conjecture,
vAPP(set_Pr1986765409at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,$o),ord_le841296385at_nat,edges),vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(f2960,plain,
( spl155_30
| ~ spl155_3
| ~ spl155_10 ),
inference(avatar_split_clause,[],[f2832,f2810,f2771,f2958]) ).
thf(f2832,plain,
( ! [X0: list_P559422087at_nat,X1: set_Pr1986765409at_nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X0)),X1)) )
| ~ spl155_3
| ~ spl155_10 ),
inference(trivial_inequality_removal,[],[f2825]) ).
thf(f2825,plain,
( ! [X0: list_P559422087at_nat,X1: set_Pr1986765409at_nat] :
( ( $true != $true )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X0)),X1)) ) )
| ~ spl155_3
| ~ spl155_10 ),
inference(superposition,[],[f2811,f2772]) ).
thf(f2952,plain,
spl155_29,
inference(avatar_split_clause,[],[f1760,f2950]) ).
thf(f1760,plain,
! [X0: set_se1612935105at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK21,X1),X0)),X0) )
| ( $true != vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X1),X0) )
| ( $true != vAPP(set_se1612935105at_nat,$o,finite1457549322at_nat,X0) ) ),
inference(cnf_transformation,[],[f1472]) ).
thf(f2948,plain,
spl155_28,
inference(avatar_split_clause,[],[f1757,f2946]) ).
thf(f1757,plain,
! [X0: set_se1612935105at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,vAPP(set_se1612935105at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,set_Pr1986765409at_nat),sK20,X1),X0)),X0) )
| ( $true != vAPP(set_se1612935105at_nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(set_se1612935105at_nat,$o),member298845450at_nat,X1),X0) )
| ( $true != vAPP(set_se1612935105at_nat,$o,finite1457549322at_nat,X0) ) ),
inference(cnf_transformation,[],[f1470]) ).
thf(f2944,plain,
spl155_27,
inference(avatar_split_clause,[],[f1754,f2942]) ).
thf(f1754,plain,
! [X0: set_set_nat,X1: set_nat] :
( ( $true = vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,vAPP(set_set_nat,set_nat,vAPP(set_nat,sTfun(set_set_nat,set_nat),sK19,X1),X0)),X0) )
| ( $true != vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X1),X0) )
| ( $true != vAPP(set_set_nat,$o,finite2012248349et_nat,X0) ) ),
inference(cnf_transformation,[],[f1468]) ).
thf(f2940,plain,
spl155_26,
inference(avatar_split_clause,[],[f1751,f2938]) ).
thf(f1751,plain,
! [X0: set_set_nat,X1: set_nat] :
( ( $true = vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,vAPP(set_set_nat,set_nat,vAPP(set_nat,sTfun(set_set_nat,set_nat),sK18,X1),X0)),X0) )
| ( $true != vAPP(set_set_nat,$o,vAPP(set_nat,sTfun(set_set_nat,$o),member_set_nat,X1),X0) )
| ( $true != vAPP(set_set_nat,$o,finite2012248349et_nat,X0) ) ),
inference(cnf_transformation,[],[f1466]) ).
thf(f2934,plain,
spl155_25,
inference(avatar_split_clause,[],[f1980,f2932]) ).
thf(f1980,plain,
! [X2: list_P559422087at_nat,X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,nat)),sK64,X2),X1),X0) = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(list_P559422087at_nat,sTfun(nat,sTfun(nat,$o)),sP7,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f1528]) ).
thf(f2916,plain,
spl155_24,
inference(avatar_split_clause,[],[f1900,f2914]) ).
thf(f1900,plain,
! [X2: nat,X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK60,X0)) )
| ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK61,X2),X0)) )
| ( $true != vAPP(nat,$o,X0,X1) ) ),
inference(cnf_transformation,[],[f1520]) ).
thf(f2901,plain,
spl155_23,
inference(avatar_split_clause,[],[f1965,f2899]) ).
thf(f1965,plain,
! [X2: set_Pr1986765409at_nat,X0: product_prod_nat_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),X2) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),X2)) ) ),
inference(cnf_transformation,[],[f1307]) ).
thf(f1307,plain,
! [X0: product_prod_nat_nat,X1: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat] :
( ( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),X2) )
& ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),X1) ) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),X2)) ) ),
inference(ennf_transformation,[],[f1057]) ).
thf(f1057,plain,
! [X0: product_prod_nat_nat,X1: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),X2)) )
=> ~ ( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),X1) )
=> ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),X2) ) ) ),
inference(flattening,[],[f881]) ).
thf(f881,plain,
! [X0: product_prod_nat_nat,X1: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),X2)) )
=> ~ ( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),X1) )
=> ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),X2) ) ) ),
inference(fool_elimination,[],[f880]) ).
thf(f880,plain,
! [X0: product_prod_nat_nat,X1: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),X2))
=> ~ ( vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),X1)
=> ~ vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),X2) ) ),
inference(rectify,[],[f161]) ).
thf(f161,axiom,
! [X9: product_prod_nat_nat,X2: set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X9),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X2),X3))
=> ~ ( vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X9),X2)
=> ~ vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X9),X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_IntE) ).
thf(f2897,plain,
spl155_22,
inference(avatar_split_clause,[],[f1964,f2895]) ).
thf(f1964,plain,
! [X2: set_Pr1986765409at_nat,X0: product_prod_nat_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),X1) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X0),vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X1),X2)) ) ),
inference(cnf_transformation,[],[f1307]) ).
thf(f2893,plain,
spl155_21,
inference(avatar_split_clause,[],[f1957,f2891]) ).
thf(f2891,plain,
( spl155_21
<=> ! [X2: set_nat,X0: nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),X2) )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_21])]) ).
thf(f1957,plain,
! [X2: set_nat,X0: nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),X2) )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),X2)) ) ),
inference(cnf_transformation,[],[f1302]) ).
thf(f1302,plain,
! [X0: nat,X1: set_nat,X2: set_nat] :
( ( ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),X2) )
& ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),X1) ) )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),X2)) ) ),
inference(ennf_transformation,[],[f1054]) ).
thf(f1054,plain,
! [X0: nat,X1: set_nat,X2: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),X2)) )
=> ~ ( ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),X1) )
=> ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),X2) ) ) ),
inference(flattening,[],[f871]) ).
thf(f871,plain,
! [X0: nat,X1: set_nat,X2: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),X2)) )
=> ~ ( ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),X1) )
=> ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),X2) ) ) ),
inference(fool_elimination,[],[f870]) ).
thf(f870,plain,
! [X0: nat,X1: set_nat,X2: set_nat] :
( vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),X2))
=> ~ ( vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),X1)
=> ~ vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),X2) ) ),
inference(rectify,[],[f160]) ).
thf(f160,axiom,
! [X9: nat,X2: set_nat,X3: set_nat] :
( vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X9),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X2),X3))
=> ~ ( vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X9),X2)
=> ~ vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X9),X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_IntE) ).
thf(f2889,plain,
spl155_20,
inference(avatar_split_clause,[],[f1956,f2887]) ).
thf(f2887,plain,
( spl155_20
<=> ! [X2: set_nat,X0: nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),X1) )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_20])]) ).
thf(f1956,plain,
! [X2: set_nat,X0: nat,X1: set_nat] :
( ( $true = vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),X1) )
| ( $true != vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X0),vAPP(set_nat,set_nat,vAPP(set_nat,sTfun(set_nat,set_nat),inf_inf_set_nat,X1),X2)) ) ),
inference(cnf_transformation,[],[f1302]) ).
thf(f2885,plain,
spl155_19,
inference(avatar_split_clause,[],[f2095,f2882]) ).
thf(f2095,plain,
vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isShortestPath_a,c),s),p),t) = $true,
inference(cnf_transformation,[],[f1031]) ).
thf(f1031,plain,
vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isShortestPath_a,c),s),p),t) = $true,
inference(fool_elimination,[],[f1030]) ).
thf(f1030,plain,
vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isShortestPath_a,c),s),p),t),
inference(rectify,[],[f1]) ).
thf(f1,axiom,
vAPP(nat,$o,vAPP(list_P559422087at_nat,sTfun(nat,$o),vAPP(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o)),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(list_P559422087at_nat,sTfun(nat,$o))),isShortestPath_a,c),s),p),t),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_SP) ).
thf(f2880,plain,
( spl155_18
| ~ spl155_3
| ~ spl155_6 ),
inference(avatar_split_clause,[],[f2795,f2785,f2771,f2878]) ).
thf(f2878,plain,
( spl155_18
<=> ! [X0: list_P559422087at_nat] : ( vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X0) = vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,vAPP(set_Pr1986765409at_nat,list_P559422087at_nat,sK9,vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_18])]) ).
thf(f2795,plain,
( ! [X0: list_P559422087at_nat] : ( vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X0) = vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,vAPP(set_Pr1986765409at_nat,list_P559422087at_nat,sK9,vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X0))) )
| ~ spl155_3
| ~ spl155_6 ),
inference(trivial_inequality_removal,[],[f2788]) ).
thf(f2788,plain,
( ! [X0: list_P559422087at_nat] :
( ( $true != $true )
| ( vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X0) = vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,vAPP(set_Pr1986765409at_nat,list_P559422087at_nat,sK9,vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X0))) ) )
| ~ spl155_3
| ~ spl155_6 ),
inference(superposition,[],[f2786,f2772]) ).
thf(f2870,plain,
spl155_17,
inference(avatar_split_clause,[],[f1747,f2868]) ).
thf(f1747,plain,
! [X0: nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(nat,set_Pr1986765409at_nat),sK17,X1),X0)) )
| ( $true != vAPP(nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(nat,$o),sP1,X1),X0) ) ),
inference(cnf_transformation,[],[f1464]) ).
thf(f2866,plain,
spl155_16,
inference(avatar_split_clause,[],[f1666,f2864]) ).
thf(f1666,plain,
! [X0: set_nat] : ( vAPP(sTfun(nat,$o),set_nat,collect_nat,vAPP(set_nat,sTfun(nat,$o),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat),X0)) = X0 ),
inference(cnf_transformation,[],[f427]) ).
thf(f427,plain,
! [X0: set_nat] : ( vAPP(sTfun(nat,$o),set_nat,collect_nat,vAPP(set_nat,sTfun(nat,$o),vAPP(sTfun(nat,sTfun(set_nat,$o)),sTfun(set_nat,sTfun(nat,$o)),cCOMB,member_nat),X0)) = X0 ),
inference(fool_elimination,[],[f426]) ).
thf(f426,plain,
! [X0: set_nat] :
( vAPP(sTfun(nat,$o),set_nat,collect_nat,
^ [X1: nat] : vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X1),X0)) = X0 ),
inference(rectify,[],[f104]) ).
thf(f104,axiom,
! [X2: set_nat] :
( vAPP(sTfun(nat,$o),set_nat,collect_nat,
^ [X23: nat] : vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,X23),X2)) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_Collect__mem__eq) ).
thf(f2862,plain,
spl155_15,
inference(avatar_split_clause,[],[f1665,f2860]) ).
thf(f1665,plain,
! [X0: set_Pr1986765409at_nat] : ( vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,vAPP(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o),vAPP(sTfun(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o)),cCOMB,member701585322at_nat),X0)) = X0 ),
inference(cnf_transformation,[],[f425]) ).
thf(f425,plain,
! [X0: set_Pr1986765409at_nat] : ( vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,vAPP(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o),vAPP(sTfun(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o)),sTfun(set_Pr1986765409at_nat,sTfun(product_prod_nat_nat,$o)),cCOMB,member701585322at_nat),X0)) = X0 ),
inference(fool_elimination,[],[f424]) ).
thf(f424,plain,
! [X0: set_Pr1986765409at_nat] :
( vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,
^ [X1: product_prod_nat_nat] : vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X1),X0)) = X0 ),
inference(rectify,[],[f105]) ).
thf(f105,axiom,
! [X2: set_Pr1986765409at_nat] :
( vAPP(sTfun(product_prod_nat_nat,$o),set_Pr1986765409at_nat,collec7649004at_nat,
^ [X23: product_prod_nat_nat] : vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,X23),X2)) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_Collect__mem__eq) ).
thf(f2852,plain,
spl155_14,
inference(avatar_split_clause,[],[f2094,f2849]) ).
thf(f2849,plain,
( spl155_14
<=> ( vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,c),s),t)) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_14])]) ).
thf(f2094,plain,
vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,c),s),t)) = $true,
inference(cnf_transformation,[],[f1029]) ).
thf(f1029,plain,
vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,c),s),t)) = $true,
inference(fool_elimination,[],[f1028]) ).
thf(f1028,plain,
vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,c),s),t)),
inference(rectify,[],[f159]) ).
thf(f159,axiom,
vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(nat,set_Pr1986765409at_nat),vAPP(sTfun(product_prod_nat_nat,a),sTfun(nat,sTfun(nat,set_Pr1986765409at_nat)),edmond475474835dges_a,c),s),t)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_finite__spEdges) ).
thf(f2824,plain,
spl155_13,
inference(avatar_split_clause,[],[f1730,f2822]) ).
thf(f2822,plain,
( spl155_13
<=> ! [X0: set_Pr1986765409at_nat,X1: nat] :
( ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sK11,X1),X0)) = X1 )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_13])]) ).
thf(f1730,plain,
! [X0: set_Pr1986765409at_nat,X1: nat] :
( ( vAPP(set_Pr1986765409at_nat,nat,finite447719721at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sK11,X1),X0)) = X1 )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) ) ),
inference(cnf_transformation,[],[f1448]) ).
thf(f2820,plain,
spl155_12,
inference(avatar_split_clause,[],[f1729,f2818]) ).
thf(f1729,plain,
! [X0: set_Pr1986765409at_nat,X1: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),sK11,X1),X0)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) ) ),
inference(cnf_transformation,[],[f1448]) ).
thf(f2816,plain,
spl155_11,
inference(avatar_split_clause,[],[f1725,f2814]) ).
thf(f1725,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X1) ) ),
inference(cnf_transformation,[],[f1094]) ).
thf(f1094,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1)) )
| ( ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X1) )
& ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) ) ) ),
inference(ennf_transformation,[],[f533]) ).
thf(f533,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X1) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) ) )
=> ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1)) ) ),
inference(fool_elimination,[],[f532]) ).
thf(f532,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X1)
| vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) )
=> vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1)) ),
inference(rectify,[],[f202]) ).
thf(f202,axiom,
! [X38: set_Pr1986765409at_nat,X39: set_Pr1986765409at_nat] :
( ( vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X39)
| vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X38) )
=> vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X38),X39)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_finite__Int) ).
thf(f2812,plain,
spl155_10,
inference(avatar_split_clause,[],[f1724,f2810]) ).
thf(f1724,plain,
! [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(set_Pr1986765409at_nat,set_Pr1986765409at_nat,vAPP(set_Pr1986765409at_nat,sTfun(set_Pr1986765409at_nat,set_Pr1986765409at_nat),inf_in586391887at_nat,X0),X1)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) ) ),
inference(cnf_transformation,[],[f1094]) ).
thf(f2808,plain,
spl155_9,
inference(avatar_split_clause,[],[f1749,f2806]) ).
thf(f1749,plain,
! [X0: set_Pr1986765409at_nat,X1: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) )
| ( $true = vAPP(nat,$o,vAPP(set_Pr1986765409at_nat,sTfun(nat,$o),sP1,X0),X1) ) ),
inference(cnf_transformation,[],[f1431]) ).
thf(f2804,plain,
spl155_8,
inference(avatar_split_clause,[],[f2092,f2801]) ).
thf(f2092,plain,
vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,s),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,c)) = $true,
inference(cnf_transformation,[],[f1025]) ).
thf(f1025,plain,
vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,s),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,c)) = $true,
inference(fool_elimination,[],[f1024]) ).
thf(f1024,plain,
vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,s),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,c)),
inference(rectify,[],[f17]) ).
thf(f17,axiom,
vAPP(set_nat,$o,vAPP(nat,sTfun(set_nat,$o),member_nat,s),vAPP(sTfun(product_prod_nat_nat,a),set_nat,v_a,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_SV) ).
thf(f2799,plain,
( spl155_7
| ~ spl155_2
| ~ spl155_6 ),
inference(avatar_split_clause,[],[f2792,f2785,f2739,f2797]) ).
thf(f2797,plain,
( spl155_7
<=> ! [X0: set_Pr1986765409at_nat] :
( ( vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,vAPP(set_Pr1986765409at_nat,list_P559422087at_nat,sK9,X0)) = X0 )
| ( $false = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_7])]) ).
thf(f2792,plain,
( ! [X0: set_Pr1986765409at_nat] :
( ( vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,vAPP(set_Pr1986765409at_nat,list_P559422087at_nat,sK9,X0)) = X0 )
| ( $false = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) ) )
| ~ spl155_2
| ~ spl155_6 ),
inference(trivial_inequality_removal,[],[f2791]) ).
thf(f2791,plain,
( ! [X0: set_Pr1986765409at_nat] :
( ( $true != $true )
| ( vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,vAPP(set_Pr1986765409at_nat,list_P559422087at_nat,sK9,X0)) = X0 )
| ( $false = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) ) )
| ~ spl155_2
| ~ spl155_6 ),
inference(superposition,[],[f2786,f2740]) ).
thf(f2787,plain,
spl155_6,
inference(avatar_split_clause,[],[f1668,f2785]) ).
thf(f1668,plain,
! [X0: set_Pr1986765409at_nat] :
( ( vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,vAPP(set_Pr1986765409at_nat,list_P559422087at_nat,sK9,X0)) = X0 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) ) ),
inference(cnf_transformation,[],[f1444]) ).
thf(f1444,plain,
! [X0: set_Pr1986765409at_nat] :
( ( vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,vAPP(set_Pr1986765409at_nat,list_P559422087at_nat,sK9,X0)) = X0 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f1065,f1443]) ).
thf(f1443,plain,
! [X0: set_Pr1986765409at_nat] :
( ? [X1: list_P559422087at_nat] : ( vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X1) = X0 )
=> ( vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,vAPP(set_Pr1986765409at_nat,list_P559422087at_nat,sK9,X0)) = X0 ) ),
introduced(choice_axiom,[]) ).
thf(f1065,plain,
! [X0: set_Pr1986765409at_nat] :
( ? [X1: list_P559422087at_nat] : ( vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X1) = X0 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) ) ),
inference(ennf_transformation,[],[f431]) ).
thf(f431,plain,
! [X0: set_Pr1986765409at_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0) )
=> ? [X1: list_P559422087at_nat] : ( vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X1) = X0 ) ),
inference(fool_elimination,[],[f430]) ).
thf(f430,plain,
! [X0: set_Pr1986765409at_nat] :
( vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X0)
=> ? [X1: list_P559422087at_nat] : ( vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X1) = X0 ) ),
inference(rectify,[],[f327]) ).
thf(f327,axiom,
! [X2: set_Pr1986765409at_nat] :
( vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,X2)
=> ? [X47: list_P559422087at_nat] : ( vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X47) = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_326_finite__list) ).
thf(f2783,plain,
spl155_5,
inference(avatar_split_clause,[],[f2090,f2780]) ).
thf(f2090,plain,
vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) = $true,
inference(cnf_transformation,[],[f1021]) ).
thf(f1021,plain,
vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)) = $true,
inference(fool_elimination,[],[f1020]) ).
thf(f1020,plain,
vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),
inference(rectify,[],[f157]) ).
thf(f157,axiom,
vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,e_a,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_finite__E) ).
thf(f2778,plain,
spl155_4,
inference(avatar_split_clause,[],[f2089,f2775]) ).
thf(f2089,plain,
vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,c)) = $true,
inference(cnf_transformation,[],[f1019]) ).
thf(f1019,plain,
vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,c)) = $true,
inference(fool_elimination,[],[f1018]) ).
thf(f1018,plain,
vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,c)),
inference(rectify,[],[f158]) ).
thf(f158,axiom,
vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(sTfun(product_prod_nat_nat,a),set_Pr1986765409at_nat,edmond771116670s_uE_a,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_finite__uE) ).
thf(f2773,plain,
spl155_3,
inference(avatar_split_clause,[],[f1685,f2771]) ).
thf(f1685,plain,
! [X0: list_P559422087at_nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X0)) ),
inference(cnf_transformation,[],[f465]) ).
thf(f465,plain,
! [X0: list_P559422087at_nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X0)) ),
inference(fool_elimination,[],[f464]) ).
thf(f464,plain,
! [X0: list_P559422087at_nat] : vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X0)),
inference(rectify,[],[f204]) ).
thf(f204,axiom,
! [X40: list_P559422087at_nat] : vAPP(set_Pr1986765409at_nat,$o,finite772653738at_nat,vAPP(list_P559422087at_nat,set_Pr1986765409at_nat,set_Pr2131844118at_nat,X40)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_List_Ofinite__set) ).
thf(f2741,plain,
spl155_2,
inference(avatar_split_clause,[],[f357,f2739]) ).
thf(f357,plain,
! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) ),
introduced(fool_axiom,[]) ).
thf(f2737,plain,
~ spl155_1,
inference(avatar_split_clause,[],[f356,f2734]) ).
thf(f2734,plain,
( spl155_1
<=> ( $true = $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl155_1])]) ).
thf(f356,plain,
$true != $false,
introduced(fool_axiom,[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : ITP050^1 : TPTP v8.2.0. Released v7.5.0.
% 0.04/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36 % Computer : n007.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Sat May 18 17:38:08 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.37 % (1205)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.40 % (1208)WARNING: value z3 for option sas not known
% 0.21/0.40 % (1206)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.40 % (1207)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.21/0.40 % (1208)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.21/0.40 % (1209)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.40 % (1210)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.21/0.40 % (1211)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.21/0.40 % (1212)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.21/0.44 % (1212)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.21/0.45 % Exception at run slice level
% 0.21/0.45 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.45 % Exception at run slice level
% 0.21/0.45 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.47 % (1213)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.21/0.47 % (1214)ott+1_9_av=off:bd=off:bs=on:gsp=on:lcm=predicate:nm=4:sp=weighted_frequency:urr=on_382 on theBenchmark for (382ds/0Mi)
% 0.21/0.49 % Exception at run slice level
% 0.21/0.49 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.50 % (1218)lrs-11_2:5_fsd=off:fde=none:nm=4:nwc=5.0:sims=off:sp=reverse_weighted_frequency:stl=62_367 on theBenchmark for (367ds/0Mi)
% 0.21/0.50 % (1213)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.21/0.50 % (1214)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.21/0.53 % Exception at run slice level
% 0.21/0.53 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 1.15/0.55 % (1232)ott+4_64_acc=on:anc=none:bs=on:bsr=on:fsd=off:gs=on:gsem=off:irw=on:msp=off:nwc=2.5:nicw=on:sims=off_354 on theBenchmark for (354ds/0Mi)
% 23.32/3.75 % (1210)First to succeed.
% 24.92/3.99 % (1210)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1205"
% 24.92/3.99 % (1210)Refutation found. Thanks to Tanya!
% 24.92/3.99 % SZS status Theorem for theBenchmark
% 24.92/3.99 % SZS output start Proof for theBenchmark
% See solution above
% 25.32/4.04 % (1210)------------------------------
% 25.32/4.04 % (1210)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 25.32/4.04 % (1210)Termination reason: Refutation
% 25.32/4.04
% 25.32/4.04 % (1210)Memory used [KB]: 12659
% 25.32/4.04 % (1210)Time elapsed: 3.584 s
% 25.32/4.04 % (1210)Instructions burned: 10594 (million)
% 25.32/4.04 % (1205)Success in time 3.646 s
%------------------------------------------------------------------------------